If there was a popping noise, then you are probably going to have to take it apart and look around inside for a blown capacitor or fuse, or some sign of electrical arcing. It could just be the power supply that has gone bad. You could try wiggling the power cord near the computer and listen for any popping noises and try to turn it on afterward if you didn't hear anything.
At any rate, you are going to need to test the power coming out of the power supply. You will need to use a multimeter. If you are averse to working on electrical circuits, then you should probably take it to a repair shop; though, it may cost more for a pro to fix than it is worth.
The link below is for an IMac G3 M4984, but it may at least give some insight on how to disassemble your computer if you are inclined to do so.
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