I must admit that I was also leaning towards a PS failure. Unfortunately I
don't have a spare but I had better get one.
Well if it was a power supply problem, then you can identify it in
but two minutes without disconnecting anything. Boot the machine and
execute programs that access all peripheral simultaneously
(multitask). Now use a 3.5 digit multimeter to read voltages on any
one of red, orange, purple, and yellow wires from power supply to
motherboard. Each voltage must read above 3.23, 4.87, and 11.7 volts
accordingly. It the power supply is reason for bad startup, then
those voltages are too low during this test.
Also measure gray wire as power is turned on. That voltage must
rise well above 2.4 volts in the first second. When computer first
does not boot, does that voltage delay? Gray wire is part of a
communication system between the many parts of a power supply
'system'. Others have assumed the entire power supply system is only
the power supply. Better is to see the failure before shotgunning
with new parts.
If voltages are OK, then move on to other suspects.
Of course, what is seen in system (event) logs? This is where
problems are identified, stored, and the OS circumvents those
problems. Therefore problems can be addressed at your leisure. Are
problems listed in that log?
Long before fixing anything, first collect facts.
Meanwhile, a second hard drive can interfere with the first one
during boot - just to complicate the analysis a little.