Completely agreed with both techknight and bbraun about recapping. I've recapped both of my IIcis and they both exhibited difficulty powering on until I replaced the capacitors and cleaned the board with isopropyl alcohol. Here's what I know about the IIci power supply:
There are at least two different brands of power supplies used in the IIci: Astec and GE. The Astec ones are known to be problematic, and apparently the GE ones are a little more reliable. I don't really know for sure. I have two IIcis -- one with an Astec and one with a GE, and they both work fine, although I've run into weird unexplainable behavior in the past with them. While researching the problems I had, I found this:
http://www.shobaffum.com/iici/trickle.pdf
I've never attempted this repair, so I have no idea if it works...
There is a way to sort of "jump start" the IIci power supply to verify that it is working. It doesn't completely work because the power supply doesn't like it when there's no load, but you can at least test to make sure the fan moves. To do this I short pins 9 and 10 (/PFW and +5V trickle) together with a paper clip. The fan will start moving slowly and the power supply tries to turn on, but I believe it doesn't fully turn on and the output voltages won't be correct (it keeps restarting because there's no load, or something like that).
