The reset often tried after a power outage or other interrupt, requires one to follow instructions in the maintenance support article regarding a reset of the Power Management Unit (PMU) as follows.
•Resetting the iMac (flat panel G4) Power Management Unit (PMU)
http://support.apple.com/kb/HT1712
This article has a few helpful images of the computer and basic explanations on how to do the procedure.
Other more in-depth items may require more take-apart know-how and techniques which will be more tedious and would follow instructions such as those outlined in an official iMac G4 Apple repair manual in PDF. These may be hard to get. While I have three iMac G4 17" 1.25GHz desktop computers, none of them are up and running at this time; my original one has a power issue and I believe it may be a failed power supply. Of the other two, one was acquired as non-running parts computer, but it has a good power supply, optical drive, display, and a few other parts. The third iMac in my instance, needs a replacement optical drive; so while I have three of these, all of them would require disassembly to remedy their various issues.
When you take apart one of these, be sure to have some new Thermal Paste, a new/fresh clock Battery, a means of re-torquing the internal chassis to required specification, and remember to remove all the old thermal paste from the heat transfer conduits before re-assembly. If you can get the correct Service Manual for this iMac G4 (several in series) which was an official Apple document, in PDF, it would be of great help in troubleshooting the issues. Some of the suggested repair procedures require access to known-good parts; in part to swap out and help find out what is not wrong with it.
Online sources of information vary, as do their worthiness and value as problem solving tools, depending on depth of the troubles involved. Even a site with info such as this iFixit may offer tips for some situations: http://www.ifixit.com/Device/iMac_G4 -- And the xlr8yourmac article on how to Take-apart iMac G4 for Drive and Ram upgrades has a few others: http://www.xlr8yourmac.com/systems/imac_g4/imacg4_takeapart.html
There are test ports or holes under the first bottom plate cover on the iMac G4 where one could use a multimeter and small tipped probes to check for correct voltage outputs from the computer power supply. There is a chance one of the power supply transformer voltage outputs may have failed.
Sometimes, a power failure may coincide with other parts failures; in example, a hard disk drive on its last legs may be affected by a power surge or outage timed upset, and that contains startup disk OS files.
To find a qualified and trained technician who can and will help repair these older models, can be a problem in and of itself; several shops also sell new hardware and their answer for an old unique computer, is to get a new not-so unique model from them. With the correct Service Manuals, you could eventually repair one of these, if you can get good quality replacement parts at low cost and do the work yourself.
Hopefully this helps somewhat.
Good luck & happy computing! 🙂
{edited to add info + url}