Chosen Solution
The motherboard is fried. Can I repair it myself?
A lot of these have the very common “bulging capacitor” issue, and that can be fixed fairly easily by someone who knows what they are doing and is good with a soldering iron. You might want to look inside to see if there are any exploded/bulging capacitors, and if so, advertise on CraigsList or elsewhere for a local tech who knows how to replace them. Hopefully this is the issue, because it’s going to be cheaper to pay a tech $100 to do a soldering job than to buy a new board, etc. Power supplies also commonly fail in these, so it’s worth exploring the possibility that that is the issue.
If your machine looks like the picture, could you look on the bottom of the stand and find the model number. If it doesn’t try opening the CD drive door and see if there is information there. The board probably can’t be repaired but it can be replaced. iFixit carries the boards for a lot of these machines and there are guides for replacing them. The G4 is harder than the G5 but with a good guide and an hour or two it’s not that difficult. With the model number I can direct you to the board and how to put it in. Could you also tell us how you determined that the motherboard was fried?
No, motherboards can generally not be repaired, even replacing them is very difficult and costly. What version iMac do you have?
