If the PSU has a tach lead coming out of the PSU (antec is known for this) then the error may indeed be the PSU fan.
A good practice for most fans is to take the sticker off the back, pull off the rubber plug if present, and put a couple of drops of oil in the bearing center and put everything back on. The reason is because most fans are sleeve or sleeve+bearing type designs, and the oil serves to keep the copper sleeve from wearing down in a short amount of time. The grinding sound you hear is the sleeve bearing and blade shaft rubbing in a dry environment, which quickly eats the sleeve and makes the fan wobble, thus making it slap around more, get hot, and lock up. Also the buildup of crud from this reaction creates a permanent lockup condition. Once it has locked up or is turning very slowly, it is too far gone to keep, even if you oil it.
I would recommend you either oil these bearings or replace all fans with bearing type designs, which last alot longer.
If you are not good with the mechanics of your computer, take it to a tech or neighbor/friend that is good with computers and have them do it. Bear in mind the programmers are not always good with hardware, I have met some that would be better off taking the computer to you for hardware servicing rather than vice versa
. So if you know a techie-type, make sure he/she is good with hardware first.
The PSU is dangerous in the sense that the capacitors are great at delivering a potentially deadly shock. At the very least it is extremely painful. I know from personal experience, I've taken the fully loaded shock from a PSU cap.
That said, if you are comfortable either replacing or servicing the PSU fan, then go for it. Otherwise find someone that can. Some techs will do it and some won't. I have no problem even replacing caps in the PSU, but not everyone is handy with a soldering iron. Replacing a fan is child's play, honestly.
edit: Let me add 2 things:
-Some PSUs have a chome grill that is mounted in place along with the fan. That means you don't have to open the PSU to service the fan. Take 3 off and spin the grill out of the way and do your thing.
-If you get oil on the back of the fan, use acetone or ethyl acetate to clean it. Fingernail polish works fine in most cases. Pure acetone can be found at walmart for a buck or 2.