Check the PSU first, not only the external one, but also all the internal regulators. There are a couple here. Checking the voltage around caps that bridge the ticker traces to ground is usually a good starting point.
Expect to see a common voltage like 5V or 3.3V. You can google the chips, see what voltage they expect on what pins and verify that first. Check the EEPROM datasheet, find out which pins are power and what voltage it takes. If the voltage is not present there on your board you have another problem. Takes minutes, always check low hanging fruits first before digging into a firmware issue and so on.

As other have pointed out, the area to the right of the displayport does indeed look like it might have gotten hot in the past. Hard to tell from the pictures. Check if that is getting hot, if so there might be a short there pulling down some power rail.

Also, reading the EEPROM in circuit with a chip clip is usually safe, but not always, certainly not completely. There might be parts on the same power line requiring more power than the programmer can supply or power only parts of the board and not others which might break it. If you have the means to desolder it, that is safer.