Chosen Solution
As I try to boot the computer, it plays the boot-up sound for a literal second then immediately shuts down. I got the machine like this. Edit: some changes
Sadly, this sounds .like the GPU board has failed iMac Intel 27" (Late 2009 or Mid 2010) Graphics Card Replacement
Take the cable (AC) out of the unit and depress the power button for 10 seconds. Plug the AC back in an try to reboot. If it exhibits the same no boot or works for a short time, then shuts off, probably is the power supply board. Just guessing :)
