Help repairing logic board 820-2936B

Hello,

My trusty 13-inch late 2011 MacBook Pro has finally had enough and called it a day after 11 years of loyal service.

Late last week while I was quietly watching a film, the screen started glitching out of nowhere and the Mac started beeping 3 times at 2-second intervals before either shutting down or restarting. This has been happening non-stop since last week. If I’m really lucky, I can maybe get 5 or 10 minutes of usage before the bugger starts again. Sometimes it’s glitching and beeping, sometimes it’s glitching alone and other times it’s just the beeps.

I’ve tried reseating the RAMs, switching RAMs, trying one RAM at a time in each slot, trying factory RAMs, trying entirely new RAMs … nothing helps. Ditto same tests in safe mode, and the Mac is still glitching and/or beeping. Working from the hypothesis that it’s a hardware issue, I ran Apple Service Diagnostics 3S148 in both OS and EFI modes but all tests came back normal. I’ve reset the PRAM and SMC more times than I care to count to no avail.

The Mac boots up in the sense that when I press the power button there is a startup chime and the screen’s Apple logo lights up. So presumably it passes POST. But then it either starts glitching/beeping immediately or after 5-10 minutes of usage.

I did notice that the battery, which I should’ve replaced in 2016 but didn’t, was for some reason causing the core CPUs to heat up to 90-100 C on startup. When I removed it and only ran the Mac on the power adapter, the core temps immediately dropped to 50-60.

So my current working hypothesis is that this continuous excessive heat has partially fried something on the logic board, but I can’t figure out what exactly. I did visually inspect the logic board for any burnt components or corrosion but didn’t note anything out of the ordinary. My brother, who’s into electronics, has volunteered to help and acquired the board’s schematics.

Where do you think we should look first?

Thanks.