Can you upgrade your processor as opposed to buying a new computer?

I have a AMD Athlon(tm) 64 X2 Dual Core Processor 3800+ and a ATI Radeon X1950 Pro video card, with 2 gigs of RAM

I want to be able to play GTA IV but my processor is too slow. Can a buy a new, fast processor and install it into the mobo?

Yes, you sure can!

But you may Also want to Upgrade your Video Card as well!!
Depending on how much you are Willing to Spend:

An Athlon 64 X2 5200+ is about $65+Shipping @ Newegg.com,
And a Powercolor Radeon HD3850 512MB Video Card is just $70 right now on Newegg!!

So, for about $140, you can Upgrade Both your CPU & Video Card.