Fixing a PCB without a schematic is tough. I've attempted that a few times but now with surface mount and proprietary programmed parts it very tough. I would guess there may be a common failure mode if several boards are failing in the same manner. Identifying that bad component or circuit may lead to fixing many of these failures.
Has anyone fixed a board?
If you can identify a chip or chips on the board you can look up the pin out and test to see if there is voltage by measuring between the ground pin and "VCC" or the power connection. Also check to see if there is a short between the positive and negative where the battery connects. I have also seen failures due to bad solder connections or cold solder joints. These can be hard to find, connect power and carefully flex the board, it may power up. If the board is dead you don't have anything to loose.