If the resistors are burning out there must be a short either on the board or wiring. Which circuit are the resistors connected to? Do you have a photo of the affected parts? I would double check the fuse ratings as they should normally be blowing if something if drawing too much current.

The HV circuit and the backbox lighting are 2 separate circuits so there is probably more than one fault. I would try repairing the board and then checking the voltages on the boards without any connectors attached first. You would need to rule out/fix any problems with the boards before connecting them to the machine.

I would be glad to help out with the boards if you need a hand.