I would try replacing the internal PRAM battery before I tried either of those two (expensive) procedures, just to rule it out. Start with the cheapest, unless you've got money to burn!
Also, I don't know if voltage is selectable on the iMac, but if it is, there should be a red slide switch close to the power plug on the back of the computer. Make sure it's displaying the correct voltage for your country (sorry, we have so many international members here, I can't assume US!).
How far into the power on process does the computer go? Does it "chime?" Does the video display anything, even for a short period of time?