A friend of mine brought in an old iMac (emc1989) that did nothing at all when I hit the power button. Having never had a power switch go bad on any Apple product, and many blogs attesting to bad power supplies on these units, I made a qiuck diagnosis.
Extremely easy swap out on these. Like replacing a battery on a kids toy. Hit the power switch and got a yellow pilot light and no start up. Hmmm. Pulled the back off again and looked closer. About 5 of the capacitors on the motherboard were swollen and powdery. Bad news. Informed the friend I screwed up and they're out 150.00 and their old iMac is a boat anchor. Good news is their hard drive is okay and the info is safe.
If there's no startup and nothing is happening. Take off the back first and check the caps on the motherboard before you buy a power supply.