I would not worry about pin offsets when you are dismantling: what I am talking about is pulling the board to get a look inside the case and under the main board to look at whether there is anything shorting out tracks.

I would suggest doing this and powering up the board with no display or drives connected to reduce the scope of the problem. With a bare main board, pull the jumpers, measure the 4 voltage rails again, and then reconnect them to see what it does. At the moment, the shutdown circuitry on the PSU seems to be working OK and it's protecting itself, so you should be OK.