If the 12V rail is stable, I'd recommend checking the 5V rail. The anet board has a 7805 equivalent surface mount linear regulator that makes the 5v rail from the 12v rail. I suspect that something has gone wrong with one of the heater mosfets and it causes the 5v rail to drop when the fet turns on. You will have to find a schematic of your board so that you can find a 5v pin to probe. The anet board doesn't have a bunch of unused pins so you might have to unplug things to find a 5v pin.
Tests to try:
Turn on the printer but do not turn on heaters, use the LCD to command movement and homing. My theory is that everything will be fine and this narrows it down to the heater circuitry.
Turn on only one heater at a time (either the bed or the hot end). Again, narrowing down to what has failed.
If you have isolated it to a single heating output, try unplugging that output from the board and seeing if it still dies. This is trying to isolate board issue vs some other external issue.
I have an anet a6 in my basement. I believe that it has the same main board as your a8. I also have a btt 32 bit board that I bought as an upgrade for the anet that I'd be willing to sell you. I'd have to look up what I paid, but pretty sure it was < $40. I also have a couple of external fet boards that you might be able to use instead of thr bad outputs on your board.
Ray Scheufler