It wouldn't be the fan, that would not affect how it starts up at first, but possible the PSU is trying to gather up energy into the capacitors and it's having a hard time converting AC to DC....
Actually, depending on the manufacturer it MIGHT be the fan. Some PSU's will NOT power up if the fan isn't spinning. The screeching noise may be the bearing going out. It may also be the HDD is about to go bad, too. Have you had any stability issues lately? As suggested above, try and pinpoint were the sound is coming from.
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