I have Fedora 18 Gnome 3 desktop running on a P3 550 MHz, 784 MB RAM with a nVidia 6200 graphics card.
The MATE DE is also installed and runs when selected from the login manager and believe it or not with
MATE running and having "compiz" and related packages installed the "desktop cube" and "emerald" window
decorator function. No this machine will not set any speed records for sure but is fun to run and test
Linux OS's on. Don't be afraid to try running Fedora and a livecd/usb would be a good way to check out
how it will or will not run.