The IIcx, IIci, and Q700 all shared a common power supply. My IIci double booted once and I've seen even freakier things in a IIcx (it wouldn't boot but after I had it plugged in for a few hours it suddenly just came on all by itself--I didn't push any power keys).

I've heard the Astec supplies in there are flaky. Try to find one with a GE, they are supposedly better.

Astec's supplies in Mac SEs were also said to be the lesser of the two. I've seen many more SEs with the Sony supply but the few I have run into with the Astec have a higher frequency of problems. (SEs are easy to tell--Astecs have white switches, Sonies have black....but this is not the case on IIcx/IIci/Q700s).