Q: My iMac G3 Dosent Start Up!!! Help Please!!

Were the temperatures high in the area where you use the iMac?

Sounds familiar...

Since this is the original iMac, I think the "flyback transformer" (the component that supplies the very high voltage needed by a CRT display), is going bad.  It's the same common reason for failure of old-school CRT televisions.  The iMac is shutting down as part of its safety design, when a potentially dangerous failure is detected.  When you disconnect it from power, and leave it disconnected for a while, the safety feature resets, and it powers up again, until the next time it happens and then it's dead again.

The component is on a board that is part of the CRT iMac that users should not access, because dangerous high voltage exists there (even after the iMac is unplugged).  Apple designed the case to make it difficult to disassemble to that point, because Apple does not want its loyal customers electrocuted.

It could also be the power supply board failing, which would cause similar symptoms.  But the flyback transformer is known to be the more common "first failure point" in the original iMac design.