No, it has PCI and PCI-e slots. It's not so much that it is old as that it is cheap.
I myself am a computer repair guy. I do wish that it did have an AGP slot for me to work with, I have a lot of random AGP graphics cards lying around. Shouldn't be too expensive to get a new graphics card.
I do also have an old Alienware computer. If I could find a way to proxy all of it's connections through the Linux computer I could use that one instead.
Thanks for the help everyone. I appreciate your efforts.
For those curious here is my setup:
KVM Switch:
Computer 1: Cheap P4 Compaq Presario. Running Ubuntu Linux, has connection to the Internet.
Computer 2: Old Alienware computer. Running Windows 7, is not connected to the Internet, is connected via Cross-over cable to computer 1.