Hi there! I've actually had quite a bit of experience with IIcis and their power supplies. With no load connected, the power supply will constantly reboot if you try to "jump start" it, so the output voltages will be all screwed up and the fan will turn slowly. Your power supply is probably fine.
I agree with bbraun about the surface mount electrolytic capacitors on the motherboard being a potential issue. Several of them are over in the area of the power on circuit on the motherboard. Both of mine experienced intermittent power problems until I removed the old capacitors, cleaned the gunk, and soldered new ones on. Now both machines work just like they are brand new.
Good luck and be sure to let us know how it goes
