Have you tried unplugging it, press power button to drain residual power and plugging it back in? You say “This is a common problem according to internet searches “ but you do not say what you have learned from it. Tell us so we won’t waste your time offering same advice.
Remove hard drive from computer and plug it in desktop computer as a slave drive to diagnose its health. If it comes up in File Explorer, run a chkdsk /f on it. Put it back in your laptop and power up. It may do another check disk on its own. If you cannot see it in another computer then you have a bad drive. If the drive is good but above does not solve your issue, remove RAM chips and unplug battery. Clean any dust around RAM, put ram and battery back in and try.
I was able to run AHT test with external monitor plugged in: I get the error4SNS/1/C0000008: TL0p - - 124. Related to the temperature sensor on LCD panel, which is odd because when I am doing the testing the lcd panel is not plugged in. That leaves me with the actual sensor on the mainboard. I have looked up my history on ifixit and this is the exact error I received when I wasted a brand new lcd panel on another iMac a couple of years ago. I think we have our answer: mainboard needs replacement because of bad temp sensor. I will recommend not replacing the mainboard as this is a late 2009 model, and the prices to get one in Canadian dollars is outrageous.
I recently replaced the glass and it did not boot up afterwards, no lights, nothing. Noticed the antenna and bluetooth cables exposed, i.e. black cable covering not there, where the cables come out of the display. I don't know how this happened but a piece of black electrical tape around the silver exposed parts did it for me.