I would expect such an overtaxed power supply to show many such issues. That alone may or may not be your issue.
Other issues are:
1. BIOS. Latest only or suffer.
2. Some other item in the brew. I once found a bad USB device that stopped the reboot. Hitting reset was the final workaround since a) it worked, b) cheap fix.
My sys boots just fine from power-off, but hangs on reboot. AMD Athlon 2100, Matsonic MS8147C MB, 300w PS.
Any & all help appreciated.