First, check the power cable. If it's loose, your problem is solved.

If not, this sounds like a power supply issue. I've had the same problem on a IIci (uses a different power supply but similar in concept with the soft switch). On the IIcx/IIci, it's possible to fix this issue with a little tinkering, but the II/IIx/IIfx would require something different. If you can pick up another PSU, I'd try that to rule out a logic board issue.