I bought a s3400f computer
http://www.shopping.hp.com/product [...] AA%2523ABA
 
Since its a slimline its very small and my video card won't fit. Can I just get a bigger case? Is it easy to do? Are there any potential problems?

You can buy half-height graphics cards for cases like these, it's not a big deal. What kind of GPU do you want to put in it? A pc like that normally has no real use for a GPU. You can get a bigger case if you want, but you need to look and see if HP is using a proprietary motherboard on this thing, in other words, something that isn't an ATX form factor. There are no potential hardware problems from getting a new case...unless you screw the installation up. It's pretty easy to do, if you research your case well enough and know your way around the inside of a computer.

8600 Gt was the best low profile card last time I checked.  But they are normally OEM and hard  get hands on. Your best bet is to search e-bay for 8600 gt low profile card.

You may also have to upgrade the power supply if you add a new video card.  A standard-sized PS may not fit in that case, so upgrading the PS could get expensive.

Look at this: http://cgi.ebay.com/ws/eBayISAPI.d [...] %3DSelling
 
Faster then your HP by alot, and $100 cheaper. You would still need a video card for highend gaming but the power supply is plenty.
 
Never buy HP ect.... for a gaming machine. The cheap ones wont work and the expensive ones are priced about double what they should be.

rr - this isn't really the place to push your systems (unless you want to buy an ad   ).