Should i upgrade my computer or buy a new one all togather

You can get away with upgrading, but I personally would start to build my own new one so I don't have to pay the mark ups on current prebuilt computers.

If you want to be able to utilize more than 3GB of RAM then you need to use a windows 7/8 x64 OS.

a new system would be better imo if you have a good budget

Or you could get a 2X4 gb ddr3 ram sticks and a gtx 750TI which you can always use in the next build if you decide to upgrade after, at least you can see how good it performs with these before upgrading.

Here is an updated list:
http://pcpartpicker.com/p/28FXMp

I noticed that the RAM I put in the previous list was Laptop memory. you dont want that

I am in the same boat as your saying, and overall the issues you first have is:
1) your running 32Bit Windows, 32Bit only can 'see' 3GB of RAM, all games and other apps need to see MINIMUM (with NOTHING ELSE installed or running on your PC) 4GB normally. So the first change would be to install the 64Bit edition IF you got it WITH your computer AND if your 'key' allowes it. IF NOT then your buying a new copy of Windows (you have to do a clean install no matter what anyway) which is $179 or so.
2) upgrade the RAM with the OS to minimum 8, better at 16GB (if your board even handles it?) if you multitask ALOT (30-40 tabs normally open in Chrome while running a audio stream, watching youtube, etc. at the same time)
3) GTX 260 is ancient and low end, it isn't worth even considering for anything and should have been replaced years ago. You could try scoring a GTX 660/670/680 if you find a deal, but most likely your going to upgrading to a 760/770/780 instead whcih leads to #3. Your looking at (no matter what) over $250
4) Sounds like this is a 'Off the Shelf' potential system (i.e. Dell, Gateway, etc.) and that means it has a CRAPPY low end cheapo PSU, outputting around 300W and the cards I listed are twice that normally (depending on how many cards you install, typing of cooling you put in, etc.), so there is another $100-300
5) The case can be of any size, and if a Off the Shelf, may be the 'wrong' size for just upgrades, which means you couldn't fit in the new GPU nor PSU, so you may be looking at a new case OR spending 2x as much to get 'authorized upgrade parts' that ONLY fit that maker's computers
6) i7s are great, last a long time, etc. and I still am hammering away with my own, problem is, there is a end of life to them all and worse the architecture has dramatically changed you can't just grab a 'new' Haswell and chuck it in, there is alot of differences on how they 'work' that requires BOTH CPU and Mobo change out.IF your a off the shelf computer your Windows is ONLY coded for that Mobo/CPU, you HAVE to buy a new copy of Windows and install it CLEAN because your 'current' copy won't turn on, won't install, etc. with the change of Mobo/CPU.

As you can see piece meal gets to be as if not more expensive than it used to, and computers are 'disposable' like Cell phone now after a couple of years, and cost 'about the same' (new PC new Cell Phone). Now if you 'Game alot' then you will need a dedicated video card, which (as noted) adds to the price in both the hardware it take to 'make it work' and just how much it costs. As you didn't indicate WHAT you use your PC for, I would then offer that if your a general user PC person, then any off the shelf i5 Haswell (including the laptops) would be the best option to replace this old system, for around $349-499 (www.slickdeals.net search for i5). If your a gamer, then you will want a dedicated video card, the path would then to buy a similiar i5 or go i7 (www.slickdeals.net i7, 8GB ram, Win8, 1TB HDD, etc. $549-799) then get the replacement PSU ($100-300) based on the video card you want (GTX 760 - GTX 880 $249-1200) and swap those into the base system and you be good to go. IF doing the hardware isnt' your thing then buying it premade would be your solution, and I would recommend one of the models you can find in CPU magazine, as these are high end gaming machines by some of the top makers (Falcon, etc.) listed with the parts so you can compare and pricing.

Throw in a new graphics card and you should see a big improvement. That 260 is OLD. Even a 750ti would be a massive improvement. As was said before, 64 bit windows will allow you to use more than 4GB of ram (which is required for a good number of games nowadays).

I like MSI and Saphire brand cards.

EVGA is a great company as well.

I used to love XFX but that was a long time ago. I haven't had one of their cards in a while. I hear that currently thier products have cooling issues.

ya the best air coolers are the sapphire tri-x followed by EVGA (on higher end cards with the ACX coolers). I water cool though, which if you have the funds its the best way to go.

If you get a 750, get the Ti version. If you get the 760, get an OC edition as they are a tad faster. MSI, ASUS, Gigabyte and EVGA are the brands I would recommend for Nvidia based cards.

For the PSU, get a seasonic or XFX. A PSU is not the place to cheap out on because a bad PSU can fry your entire system. 550 - 650W would be perfect for your system.

For ram, I love my Gskill Ripjaws X. It is cheap, reliable, and fast. Here is the actual set I recommend: http://www.newegg.com/Product/Product.aspx?Item=N82E16820231428

that antec power supply is a high quality unit so your good to go. i personally think you would do fine with a gtx760. your i7 920 "might" bottleneck slightly in some games, but my brain tells me it is still somewhat equal to a sandy bridge i5.

otherwise, you really need to back up everything important, and reinstall windows with the 64bit version using your same windows key.

what exactly is your ram? do you have a 1gb stick and a 2gb stick totaling 3gb? you should really get 8gb total and you would be good to go for gaming. at 1080p, after windows, and maybe a few apps open, games like battlefield 4@1080p on a gtx760 will fill up 4gb of system ram. so if you intend on running the graphically demanding games of the past couple years, you will want 8gb.

that all said, you would be best advised to wait for nvidia to officially announce their new maxwell line of gpus that are rumored to be arriving very soon. we should know officially in the next couple weeks at the latest. its is highly likely the gtx760 will fall in price as vendors get ready to fill their shelves with the new products, so you can get a sweet deal and save some money on whatever gpu you decide to get. with that saved money, grab yourself 8gb of ram.

also if we knew the model of your motherboard, you might be able to very safely get a modest overclock on your i7 with an inexpensive but effective cpu cooler.

as far as what brand/model gtx760... for you i would just get whatever is the cheapest out of the evga acx, msi twin frozr, gigabyte windforce, or asus dc2. i currently see the msi the cheapest and it is a wonderful card. at any rate, the gtx760 is a relatively low power low heat generating card, and any one of the models i listed is going to perform very will with low temps and quiet operation.

PCPartPicker part list / Price breakdown by merchant

Video Card: MSI GeForce GTX 760 2GB TWIN FROZR Video Card ($219.99 @ Micro Center)
Total: $219.99
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2014-09-12 14:02 EDT-0400

but like i said, if you can, wait for nvidia to show its cards and you can save a few bucks, you will definitely want 8gb of system ram and 64bit win7 installed. after all that, your system should be good to go for gaming for at least the next few years.

Typically I buy yesteryear's equipment because Manufactures always charge stupidly insane prices when something first comes out. Especially things like CPU and GPUs.
I dont see where your old monitor would be a problem. in my Test rig on my workbench I have an old 14" Dell and I have hooked everything up to it. I even plugged it into a new build once that had a Titan in it. it works just fine.

nah, there is a huge gap. a quick search on Newegg showed the cheapest 970 to go for about $330 while the cheapest 770 I saw was about $250.

Just butting in.
As has been said, the current CPU is still solid, I'll suggest you hold onto it, at least until Intel releases their new Broadwell (codename) chips, sometime next year, then see if the upgrade is cost effective.
The I7's of that generation usually used triple channel memory so memory modules should be installed in threes, not pairs as is the current norm. It is possible to install in pairs but some performance will be lost.
Some windows install discs have both 32 and 64 bit on them, so you may be able up upgrade to 64 bit without purchasing a new license or media, check the disc and pop over to the Microsoft website for more detailed information. Also check the 'Anytime Upgrade' option Start>Control Panel>System and Security>Anytime Upgrade and see what it says.
Both the GTX780 and GTX970 will be heavily held back by the current CPU, even if it is strongly overclocked so unless you plan on a full CPU/MB/RAM upgrade in the future and intend to carry the new card over I'll suggest you look at the R9 280 or GTX760 as upgrades, they're a much better match to the current setup.
Overclocking is something I feel you should at least look into, experience with my dearly departed i5 750 clearly shows that at stock speed chips of that generation restrict even R9 280/GTX760 cards at 1080 rez, perhaps you might want to start a new thread in the Overclocking Forum to get more information/suggestions on the subject.
My suggestions:
Switch to Win 7 64 bit and add memory to bring it up to either 6Gb (3x2) or 12 Gb (3x4). Overclock the current CPU. Upgrade to either a R9 280 or GTX760, bear in mind that some may require 1x6 and 1x8 pin PCI-E leads and the installed power supply has only 2x6 pin, so check the specs carefully.
You could go to a GTX970 on the existing PSU, but not a GTX780, it has higher power demands and usually needs at least 1x6 and 1x8 pin PCI-E power leads while the GTX970 usually only needs dual 6 pin leads.