Tater wrote:

Is it possible that running the computer for months (maybe over a
year?) with the power supply air intake clogged has degraded the power
supply and it is in need of replacement?

The electrolytic capacitors (according to one supplier),
will last 15 years with a moderate temperature rise.
After 15 years, the rubber seal on the bottom of the
capacitor tends to degrade and allow the electrolyte
to dry out. It's not a guarantee they fail in year 15,
but it's a guesstimate. For example, if there was ozone
in the air, the life could be shorter (ozone attacks
rubber).

Life can be as short as 2000 hours, if you run them
close to the boiling point of water. That would be
four months of 8 hour days of Furmark.

I can't begin to guess how hot it got, but if the
overtemp is switching it off, it got pretty hot.

You're using the right approach - test and look
for issues, with the max electrical load you
would normally use. If you still see instability,
and occasional switch-off, then replace it. Being
careful to orient the new supply a different way, when
you install it :-)

Paul