Is my computer upgradable or should i get a new one?

Well, I think the most important thing here is, what case, and power supply do you have?

I think the only upgrade here is a new Motherboard, RAM, CPU and Video Card.

This is 100% the build I would recommend. However it looks like his current PC is a custom build. It could have a suitable PSU and Case. Even a 5 year old Hard Disk could be 500GB and decent enough for him to use for a bit. Remember the 1060 is pretty light on power.

My PSU from an '07 build is 500w and could easily run the system you spec'd out above.

Good call, if you already have a hard drive, and a suitable PSU/Case, you could definitely cut down on costs. Assuming all of those things are compatible with the new system, the build I suggested would only be $724.93. And if you already have an optical drive on top of that, you'd be sitting right around $700.

Swap the Kingston V300 for Adata SP550 of same capacity.
Swap the Ripjaws 2400 for the Aegis 2133.
Use the saving from those to switch the CX600 to S12II 620.
A H170 board is excessive spending at his budget. A B150 board like ASROCK B150M Pro4 or MSI B150M Mortar is perfectly fine for his usage.

Everything is upgrade-able, but I doubt you would be satisfied for gaming. If I were determined to try, you can upgrade the CPU, memory and graphics card.

CPU: Check with ASUS for a recommended (supported) list of CPUs.
http://www.cpu-upgrade.com/mb-ASUS/P5G41T-M_LX.html
The Q9650 looks like top dog. That's your best safe bet. Always nice playing safe. If you want to experiment, here you go. Your MB has a 775 socket, which may allow a wide range of upgrades. I don't know from experience which are compatible, but from benchmark charts I would investigate the top performers. I would look at this chart:
http://www.cpubenchmark.net/socketType.html#id5
There are slightly faster XEONs in the 771 format, which I have successfully used on my older 775 motherboard, but you have to put a mod on the CPU and the socket, and it's not for sane people. I used an X5470 with both mods, after making sure someone else had verified it would work. Very happy. I do know that some similar CPUs would not work in my particular MB, so it is a gamble.

MEMORY: You have two slots which are DDR3 1333 compatible. Get 2x4GB sticks of good brand DDR3 1333 RAM. You may have to manually tweek Setup for the RAM. You will have to upgrade the OS to 64 bit to address it. Here is more:
http://www.tomshardware.com/answers/id-2455631/ram-working-asus-p5g41t.html
http://www.crucial.com/usa/en/compatible-upgrade-for//p5g41t-m-lx

GRAPHICS: You have a PCI Express x16 slot, so most graphics drop in. Get the best you can afford. The best changes daily, and the high end ones will cost a lot and require you to go to a higher wattage power supply, say 500-700 watt and maybe extra cooling fans. Here is a chart which is valid for now, but soon will be obsolete.
http://cdn.mos.cms.futurecdn.net/7Nruuy2mJtvfwnzEfQpegf.png

I would do the memory first, then CPU, then graphics card.

Depends on the brand, if it's a reputable brand and is really making 500W, then you'll be fine. If it's not so good a brand, you may need to get a better one.

You might want to post your PSU model here just in case, but 500w is enough wattage.

The reason that you want to upgrade your motherboard is for the CPU.

You are using a board that has an LGA 775 socket. Intel abandoned that one a while ago, so you won't find any current generation processors using it. In order to take advantage of the new Skylake CPU family, you need a board with the Intel LGA 1151 socket.

This forum is great for the expertise you share. I think the recommendations for a new system for gaming are ideal. In my case, I did not need a gaming system, just a more faster, more reliable one. I also wanted to reuse as much as possible of my old machine and spend less, so I followed a different path which I will share with you.

I have an ancient system, an old HP M9300T from 2008 running windows 7/64. For many reasons, it needed an upgrade. I thought a lot about this, because I had a budget in mind and wanted to keep most of my old hardware for environmental reasons. I wanted a performance kicker at low cost. In short, here is what I did. I did 4 upgrades: I doubled RAM size, upped CPU speed, added an SSD for system software, and put in a much faster graphics card. I am extremely happy with the result.

I doubled memory size and dropped in a faster CPU. I had only 4gb memory, so I went to 8gb, the max for this motherboard. My motherboard is old with a 775 CPU socket and G33 chipset. After research, I found the fastest CPU that was known to work in this motherboard was a Xeon x5470. It is a 771 socket chip, so a couple of mods were needed to make it work. I used a small flex circuit adapter to convert the pinout from 771 to 775, and I nibbled the socket plastic keys off. Raw CPU performance is up 50%, and more memory makes Photoshop handle large images much faster. Memory cost $32, CPU plus adapter cost about $51.

I put my system software on a small SSD drive and left data on my original 750GB hard drive. My system is old, and it's on 24/7, so unfortunately I have had 2 hard drives fail and wanted a more reliable drive now. I used a small Intel 180GB SSD. I could have used a larger SSD, but I only had about 35GB of system software so this was adequate. I had to do a new install of all software on the SSD, and make the SSD have priority in BIOS Setup, but after some fiddling this worked amazingly well. I went from boot times of 3+ minutes to under 30 seconds, and all operations sped up. Cost was about $37 for this small SSD. I highly recommend this mod for any system - the speedup is dramatic.

My graphics card kept overheating and shutting down the system on very hot days, a known problem with the card (MSI GeForce 9500 GS). HP already replaced this once due to fan bearing failure problems. They did this for free even though my system was out of warranty, so I thank them for fixing a lemon. But the fan wore out again and I had to cobble a replacement fan. It kept overheating. PC Wizard said the GPU was very hot, over 110C, even on cool days. I decided to get a better graphics card, There are so many fantastic choices, but I had some constraints: size and power. My case is cramped with excess cabling, so a long graphics card would be awkward. I did not want to have to upgrade the Power Supply, so I had a limit for power. I decided to use a compact card with moderate power consumption, I settled on an NVidia 960 GTX. My heating problem was solved and the graphics performance is much better, much more than I actually need, Cost was $107.

I met my goals, to enhance performance, to minimize cost and to re-use much of the system. I'm pretty sure this would be a lousy gaming machine, but for my needs it's just fine.