XPS 8700 upgrading graphics card

I own an XPS 8700 (i7-4770 w/12 GB of RAM) and am possibly looking to upgrade the graphics card (currently a GTX 645).  When playing games, even ones that aren't very intensive, I'm getting a lot of artifacts and crashing.  The computer is only about 5 years old, so I would like to squeeze a few more years out of it if possible.

Is it reasonable that the problem is the graphics card, or should I be looking at something else?

Assuming I should move forward, which card would be a good replacement?  I'm looking to spend as little money as possible, but I would like to be able to play pretty much any game that's out there.

Am I going to run into problems with BIOS, needing two slots, etc. etc.?

Thank you very much!