PC power supply fan

[Athena]

Quick question for you tech junkies: I have an old Dell PC, circa 2002 or so. It's been shutting itself off lately, and I think it's due to overheating.

I opened it up, and sure enough, the CPU cooler fan is not starting up anymore. But the fan on the power supply doesn't seem to be starting either. It does boot up, so I know the power supply works. So my question is, should the fan built into the power supply come on right away, or is it normal that it doesn't start up when the system comes on?

For what it's worth, same question for the CPU fan. I assume it should start going when the system turns on... right?