What I am puzzled by is a dead power supply should just be dead, no light on it and it would not restart later or under any circumstances. Usually if a pump works randomly, the issue is elsewhere. It is probable that now the power supply is dead but the past incidents are most likely due to one of the following:
1) Potentiometer on the pump is turned down, this should always be at 100% when a controller is used, otherwise they overlap and the pump can be turned down too far to run and start.
2) The drive unit is siezed by calcium, the replacement should rule this out though.
3) The controller cable connection is loose or faulty, try with no controller connected to rule this out (unplug cable at the pump, a dead end cable from the pump will also cause issues).
4) The motor is failing.