My 27" late 2009 iMac will not power on. Prior to this it had a couple of issues of screen going black. Advice please!

Today my late 2009 iMac went blank, then I got a picture again, then it went blank and I had to turn it off and restart using the power button. It then worked fine for a few hours, until the same thing hppened again. The screen flashed on and off a couple of times, then stayed off although I could hear the fan and that it was backing up. When I could hear the backup had stopped I turned it off with the power button, checked for over heating, then left it a few hours. I cleaned out the vents, unplugged it from the power supply for a few minutes, then reconnected and tried to power on. Absolutely no response. PleApple service centrease can anyone tell me what to do?