I am usually a console gamer, but I was just curious as to how well my PC would run Fallout 3 or New Vegas. The computer just sits there and I want to use it for something.

It is a Gateway
The processor is AMD Phenom ™ Quad - Core 1.8 Ghz
RAM is 4 GB
Video Card is ATI Radeon HD 3200 Graphics.

I think my hangup will be the video card, but any opinions would be appreciated.

The Video Card needs to be upgraded if you want to run it without lags or if you want to run it at decent levels. ATI Radeon 3200s share their memory, meaning that they also acquire some video memory from your RAM. This is useless on graphic-intensive games. Try to find a Video Card that's around 512 MB of video memory, dedicated. 1024 MB can be a choice, too. However, do note that ATI Radeon 3200s are integrated, meaning that they are fixed on the motherboard. The RAM is fine, regardless of the RAM frequency. The processor is a Quad Core, so It should run nicely.

I dunnot its a 1.8 ghz AMD. (the minmum specs on the site say CPU: dual core 2.0 GHz) that would be pushing it. it would run but i cant say very well (atleast in combat)
the engine does run multiple threads, but having a quad core wont make up for the raw power needed for the main thread to run correctly (which will alway run off one core, hence the need for the 2ghz)
(thats not even going in to the Calcs per cycle disadvantage hes at having a AMD cpu. )
not bashing AMD, I love their CPUs / GPUs. but its a FACT they run slower Clock for clock than Intel CPUs (atm, cant wait to benchmark a Bulldozer Zambezi CPU to see how they Stack up (i hope they blow the doors off the Sandybridges. Intel has been on top for far too long ))