My 20" mid 2007 iMac has started to make a chiming (beeb) when waking from sleep. Last night when waking it shut it self off and now today I notice the chime, it is a single chime or beep and quite faint.
Try shutting down, and when powering back up, hold down the power button until you hear a BOOOOOOOOOOOOOOOP noise. Release the button when you hear that.