Power supply dying?

[Stavka.CCCP-Red Army]

I have an older Core 2 Duo desktop that I use for ripping movies, etc.
The system was running fine until about a week ago when it simply shut
down. I thought it might be a power bump and I had forgotten to set the
BIOS to restart on restoration of power. However, when I tried to
restart the system it started the boot process, got through initialising
the PCIe video card and just before the POST screen came up it simply
shut off.

I then checked the fans - CPU, video card and two cooling fans - and
they are both "free" (no resistance as if there was dust in the bearings
- a use HEPA filter paper over all the intakes - boy do they get dirty!)
and they were fine. All the fans are working fine

I've reseated the two OCZ 2GB DIMMs

I've removed the only card (a old ATI TVwonder VE PCI card) in the
system - still shuts down.

I've also removed the three hard disks to see if there was some issue
with the hard disks. They all show up on POST.

I don't think that the power supply has failed. It is relatively new -
about two years or so. There is not any burning smell.

Suggestions? The motherboard is an Asus P5W DH Deluxe with a 2.4 GHz
Core 2 Duo E6600 CPU.

This one has me stumped...

Thanks!