Nice picture of the CPU board, but the outlook doesn't look so good, I was suspecting that there is some FPGA involved and it is, it looks like the SMPS for the small voltages you've measured is working OK, and I believe the whole board is feed via 3V3 or 5V on pin 1 where the huge ferrite bead is, if it's anything else besides 3V3 I'd search for it on the board, because the ST MCU needs it for the I/O and most likely the FPGA too, if the 3V3 it's there OK, then there is no otter option:
It's HEADER TIME !!!or else, due to BGA and hi-density packages
You can't touch this !!!Joking aside, I bet that the 8pin header is the JTAG (most likely if you have Xlilinx programmer, you'll be able to read the chain) and that the bottom one has a lot other goodies, like serial debug for the CPU, voltages and interesting signals, so if push comes to show, populate them and start measuring.
Barring some other subtle power supply, connector or soldering issues, your only bet to repair the thing is to be a botched firmware update, and nowadays nobody bothers with dual firmware images and recovery partitions anymore, if it's dead you throw it away and replace it or fleabay it.
But it'll be a lot of pain to get a working firmware from somewhere.
Now you really need Santa to bring you a box of luck, a most vital repair ingredient.