I just replaced a power supply on my wife's PC on Saturday. Last week a
car accident took out a transformer near our house. She said the power
went off/on three times very quickly. In our case the fan didn't run but
a LED indicator light on the power supply still came on. The PC wouldn't
even try to boot. It could be that your power supply is starting to get
flaky so it might be a good idea to replace it anyway, assuming that the
computer is of value to you.
In our case her PC was a HP that we inherited. The large motherboard
power connector was longer than what I was accustomed to. The kid a Best
Buy said that the newer power supplies have a 4-pin extender for
motherboards that have the longer plug. They are easy to replace.