I just recently had to replace the logic board on my 4,1 (flashed to 5,1). Tore it down to the minimum specs as per the Apple Tech Guide and as soon as I installed the Processor Tray I was getting a flashing white light on the power.
It was either the PSU, the logic board (backpane), or the Processor Tray. I bought another cheap 4,1 Mac Pro that was running well and started replacing parts just one at a time. Only thing that fixed it was replacing the backpane.
Unfortunately, there was very little I could do to diagnose this besides replacing the pieces one by one.
Thankfully, I can now just order a replacement backpane and then rebuild the “new” Mac Pro and repurpose it or sell it.