Chosen Solution

Non responsive to start up key combinations. Shuts down. Update (08/23/2021) iMac 27" Late 2009 16GB RAM, 2GB Hybrid Drive 2GB Gets half way through startup - there’s a slight click and the machine shuts down regardless of the key combos being held - even Target Disk Mode

On older imacs I would put new thermal paste as it’s probably dried up by now and can be over heating quickly and causing the shut down. Another possibility is a failing Hard Drive, altho this usually won’t shut down the computer you would just get a folder flashing or a circle with a line through it. I’m curious to know if this helped you. Keep me posted. Thanks