If it's a "groaning fan", the next step is a failed fan ... would you believe I'm STILL using a PSU that suffered a traumatic shutdown from that very problem - I'm amazed it survived, and it's gone back in after two failed replacements (with a new fan).
It's not really a difficult job to change the fan in a PSU, I'd recommend soldering the joins, having slipped sleeving over the wire to pull back over the join, but twisted and electrical taped would just about do. Sleeving, held in place by being tight, taped or heatshrink, is a lot better than electrical tape on it's own.
There can be enough voltage left in some of the capacitors to give you a dangerous jolt, but on many PSU's, its easy enough to keep clear of anything (including the heatsinks!) that may be connected to them.
If you hit the PC Power button after disconnecting the mains, that will normally deplete the remaining charge in the PSU.