My advice columns tend to sit on the difficult side, as I am completely unafraid of disassembling anything at all. I assume that you know the basics as far as removing the power supply and other ancillary components. I'll say it more than once: if you're not confident when working on electronics, you might not want to try anything more in-depth than module (power supply/drives/NuBus adapter/RAM) swapping. Messing with power supplies could get you hurt. Consequently, you're free to try the more invasive procedures at your own risk.
Here we go!
First, pull the PRAM battery and disconnect the power cord. Let the machine sit totally unpowered for an hour, or a day, or however long you're content to leave it alone. Then, plug it in without the PRAM battery and see if it boots. Proceed if it doesn't.
Next, check for odd smells or obviously damaged components. I suggest sniffing around the power supply's vents especially. Smell is a very important indicator of failed components that aren't readily visible. Any strong, burnt odors would be reason for concern.
If nothing is apparent, try swapping power supplies with another IIsi. It's been a while since I've had access to my excessive collection (so don't hold me to it), but the power supply from a IIci/cx/vi/vx/Q650 may also fit, though you'll have to remove the motherboard from your IIsi to use a different type power supply to test it. Again, it's been long enough that I'm not 100%, so try power supplies from different models as a last resort.
Once the temporary power supply is in place, try and turn on your IIsi. If the motherboard is out of the case, you'll probably need to have a monitor or something connected to see if it's running.
If it turns on, proceed with the next step. If nothing happens, then there's a good chance it's your motherboard. Check again for leaking capacitors, bridged traces or connections, or bad accessories (drives, NuBus adapter, RAM, etc). There's not much else to do once the logic board is found to be faulty, so the best option in that case would probably be to hit up eBay for a new board and/or new IIsi (whichever is cheaper).
If it turns on when you try to power up with the temporary power supply, there's a good chance the old power supply was bad. If you've been doing this for a while, and find youself without a spare, you can crack the old one open. Again, only do this if you're comfortable and well-versed with the necessary safety precautions required. Once you're in there, check the fuse (close to the power cord connector), and look for leaking capacitors. If the fuse is bad, replace it. Try and find one as close to the original as possible. Replacing capacitors is often only worth it if there are no viable replacement power supplies, so if capacitors are dead, I'd suggest getting a new power supply. If everything looks ok and it still doesn't work, you should probably try and buy a new one from eBay or the Forum here.
That's all I can really think of. If none of this helps, then you're probably out of luck. If you try any of this, be safe, and good luck.
Good luck with the IIsi.
