Failing PSU or Motherboard. I lean on mobo because of the fans spinning and the dvd tray opening
My bet would be on the PSU since fans are "dumb" devices that will start turning as soon as they have sufficient voltage, fans spinning is no indication that supply rails have reached power_good status. The DVD drive might not have under-voltage lock-out or not be powered by one of the rails that is failing to power up properly.
Computers and other devices with SMPS randomly shutting down or failing to power up is a very common symptom of failing output capacitors in the PSU.