The PSU on out 24" iMac was failing and would only power on once every 30 or 40 tries. The problem was getting steadily worse as time went on.
I ordered a replacement supply from iFixit which arrived in the mail 2 days later. Spent 15 minutes start to finish replacing the PSU and now we are back in business! I have replaced these several times before on other 24" iMacs so the I've had plenty of practice with this particular surgery thus the 15 minute repair time.
If your iMac PSU is starting to fail, don't wait, order the replacement supply today and be done with the problem.