Compaq power supply failure

The box I use at home is a Pentium II Compaq full tower (built like a
tank and weighs like one).
Outdated as it is, it runs fine with Windows 2000 pro SP4, with all
programs such as Nero 6, Firefox 2 etc.

It recently began this problem of every now and then not turning on
when the ON button is pressed. However, sometimes it would turn on
several minutes afterwards. I'd been suspecting something wrong with
power supply all along.

A couple of days ago it turned on after a long delay (one hour or so
after I'd pushed the ON button. But no memory check, no booting,
nothing. The monitor was not receiving any signal. Plus, the POWER ON
indicator was blinking (2 seconds on - 2 seconds off -2 seconds on
etc).
I turned it off. Now whenever I turn it on, it comes on (fans running,
LEDs on but that's all: no booting. It seems power reaches the devices
(I tried ejecting CD, it responds fine).

Could it means I've lost the power supply? strange, considering that
the system powers up convincingly, with all fans (Processor and Power
Supply) running and LEDs lighting up.

Anyone came across this? please assist.