IIsis have lots of strange issues, from the keyboard woes discussed in Charles Rubin's "What do I do Now?" books to strange power problems.

I've had something similar with a IIsi where the speaker doesn't work and/or the green light doesn't come on. Everything else works fine though.

I also had a somewhat similar problem with a IIcx a while back. It abruptly turned on after being plugged in for a half hour or so. It refused all of my keyboard and power button requests to turn itself on before that.

My guess is a capacitor problem somewhere, as they seem to be the culprit behind most of the oddities on older Macs as they age. I don't know how much research has been done with IIsis and their capacitors but if someone wants to investigate further that would be great.