First check the diagnostic LEDs [http://www.ifixit.com/Answers/View/154115/Why+wont+my+iMac+turn+on|answered].
If they are good you may have a HD problem -corrupt, full or failing HD's will cause a machine to slow. So will running lots of applications. Unlike WinDUHows when you click the red button on an app (if more than one window can be open at a time), it does not automagically quit. Check the throbbers on the dock, look at Force Quit or the Activity Monitor to see if you have more than your expected apps running).
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