Hi, it's still possibly the PSU. One of the requirements for the POST to complete successfully is that a 'power good' signal is received within a specified time. If it is late, the boot sequence will not complete. If the PSU is getting old, it may have a leaky cap or two.
Another possibility. Have a look at the electrolytic capacitors on the motherboard, especially if there is a large group of them surrounding the processor. They should be cylindrical with flat tops. If they show signs of bulging (we call them fatcaps) or leaking (like a brown coffee stain on the top or bottom) , then the motherboard is u/s. Not sure of the make of your board, but we see it a lot on Jetway and MSI boards.
Does this problem only occur if you perform a cold start rather than a restart?