Appears to be totally dead
It started running slow recently, then I got the flashing globe / ?. After a couple of attempts to repair OS from start up disk, I plugged USB drive in and managed to load OS on that. This allowed me to connect to internal drive and verifying it showed it to be in good health. I left the imac running last night still connected to the usb drive and running a recovery application to recover some photos. This morning it was off. Checked power cable, fuse etc. Pressing on / off button does nothing. Age - about 30 months -
Would it be heat related - it had been running the recovery application most of yesterday. Appeared to be running okay. Running from the usb drive.
Would it be the internal battery? The imac did tend to be on or sleeping most of the time i used it.
Take the frame off and look at the diagnostic LEDs to the right of the RAM slots and let us know what you find. Here's how to get the screen off: Installing iMac Intel 24" EMC 2267 Hard Drive Replacement
Here's how to get the bezel off: Installing iMac Intel 24" EMC 2267 Front Bezel