The power supply is rather dangerous. Capacitors storing large amount of energy can cause burns when dischaged over skin, or unfortunately, a stopped heart. Dissecting the power supply is safe if you know what you are doing, but if you are asking this you shouldn't be doing it.
if you ever want to open the power supply of a computer...
(1) ALWAYS disconnect everything
(2) Discharge all capacitors using a resistor (NOT A SHORT) (Protect yourself with gloves!)
usually, in a power supply, if it ever fails, then most likely the capacitors are dead already, so not useful salvaging it. the transformer is usually OK unless your power supply died of releasing magic smoke. the heatsink is usually strudier than anything else. fan usually works. the power plug and fuse unit is quite expensive to buy for hobby crafters, take that out and use that if you need it as well. voltage regulators are usually intact in a failed power supply, but you usually need to desolder it and take it into a new circuit..
that's about it...