I just bought a new computer!
Intel Core 2 Duo E6300
P4M800Pro-M Motherboard
1.00 GB RAM
GeForce 6800 XT (had this one for a while)
It's not all top of the line, but it's the best I could find for my AGP video card, without dropping another $200 for a video card, and some more for a higher CPU etc. Overall I am happy with it.
The only thing I have left to get is a new Power Supply. My new computer is more demanding of my 350 Watt than my last. :)
EDIT: Agh. Being that it is a $50 motherboard, only 1GB of my RAM will be stable. With two gigs Oblivion and my internet become very unstable, and crash constantly, but I am quite sure I have fixed this. I just played for 3 hours straight without any interruptions, which hopefully means the problem is over with.