Not without a lot of work. I'm pretty sure it's been done but those cases (and the Apple logic boards) are not ATX standard so it's not like the screw holes/apertures for ports etc line up.
Edit to add: for example
The machine is probably done. Any way you look it it, buying a PC or a real Intel Mac is going to be cheaper.
Have a fried with an upgraded 500ghz Powermac G4 to Sonnet 1.8ghz G4 and upgraded video card.
He's very happy.