Can I run my 460GTX on a seperate PSU?

Yes you can. You connect to one power supply just the video card. Its like you have a 700W power suply splited in two 350W.There are on the market cases in what you can put two power supplies for the same reason i think.

Those are rare and not the best solution. You can splice two power supplies together but I won't tell you how or where to go to find out because it is a very bad idea. Get one good psu and don't look back. I spend $210 on the psu I got for a reason. 1000w gold rated very high quality from NZXT.

2 350 watt power supplies do not equal a 700 watt power supply. (well maybe a cheap no name 700watt PSU that could go up in flames and take all your other hardware with it)
There is second more important consideration about power supplies that GPU manufactures take into consideration when they recommend a minimum size to run a certain card, the amount of amps supplied by the PSU on the 12 volt rails. Firstly, you need enough total wattage to power your entire system, as most people are aware of. Second though, you have to have enough AMPS running at a high enough efficiency to provide a clean power stream for the GPU on the 12 volt rails. Most PSU's under 450 watts simply don't have enough power to meet this secondary, but very important requirement for mid or higher end GPU's. A 460 may run off a secondary dedicated 350psu if it is of high quality, but all in all, its just not a great idea to do this, but there are places that will tell you how, if you want to risk it. If works, great, if it goes up in smoke, well we didn't tell you how to do it here!
Just to be correct though, there indeed are secondary power supplies out there that can double up into a case. They are made to fit into the drive bays, and they are designed specifically for this purpose, to plug in and work along side your existing PSU providing the power needed exactly for this, a high end GPU or multiple GPU configurations, or other additional power needs. But to that end, if you need more power, and you have to buy one of these, you might as just as well buy an complete new PSU, you are going to spend the money anyway.

I've looked into the GPU-dedicated power supplies, but unfortunately Newegg is out of stock on all of them.
The extra power supply I have is a Dell L350N-00 out of a Dell computer that is no longer in use, and I never had any problems with it before (it was just about the only part of that computer that actually worked well). I think for now I'll try to use it, and I'll get a better PSU once I get some extra money.
Thanks for the input guys, Happy new year.

Dude, get a good new PSU. Then, you will never have to worry about it again. Im a fan of Cooler Master Silent Pro, the 600W sells for $100, but there are cheaper options. And you may sell your 2 current PSUs on ebay to cover the new one.

The XFX Core Edition gets a 9.5 jonnyguru performance rating and will cost ya a net $60 after the MIR.

http://www.newegg.com/Product/Product.aspx?Item=N82E168...

^ +1

From personal experience I can recommend the Core Edition.

I crrently have two power supplies connected to my system and I have this switch to start the second power supply which is something you have to consider since the second power supply does not start by itself just because it's pluged in. This is an easy and convienent way to do it.

http://www.performance-pcs.com/catalog/index.php?main_p...

Defiantly yes you can all you will have to do is use a paper clip and hot wire the PSU that is only powering your GPU simple and you can run it indefinitely or if I may suggest until you can afford a new quality PSU that will power up your whole rig.

Cool I did not know that existed LOL but a paper clip works fine as well but my is that thing you suggested ever ideal.

Alright well, new PSU it is. Thanks everyone.

They make a cable for that
http://www.frozencpu.com/products/5637/cpa-167/Lian_Li_...

do it properly new psu no skimping seriously

Now you do have the info on how to do it, but if something goes up in smoke and takes $500 of your hardware with it, don't say we didn't warn you.

I ended up just buying a new PSU. I got a 650w Antec for $67. My graphics card runs great now.