How do I clear everything off an old computer and restore it to factory specs? So I can give it to someone.?

It depends on what u want to clear, whether is the CMOS settings or Hard disk.

Clearing the CMOS
When the computer is booting, continue pressing "delete" Key (in some computer, you use F8). Use your arrow keys to scroll down to Factory settings)

Clearing the Hard Disk
The best way to clear every thing on hard disk is to format it.
You can use your XP Cd or Vista CD to do it.

Should i reformat my hard drive or reinstall windows after a problem

No, Most problems can be solve. Reinstalling or formating should be the last option you consider.

What do i do if my PC can't remember the time of day or current date?

The battery on your motherboard that powers your CMOS chip has died. This happens after three to five years. You will need to turn off your PC, open the case, and look for a small lithium battery on the motherboard. It’s usually easy to find, but your computer manual may point you directly to it. Remove the battery and take it to the store, where you need to find a replacement. Pop the new one in your PC and close it up -- You are done.Unfortunately, you will have lost all of your CMOS settings, so its good idea to keep a written record of all the CMOS data before disaster strikes. Some utility programs (Such as Norton utilizes) also save your CMOS settings to disk.

Can i recover deleted or lost files

Sure you Can. In windows, you can recover most files you ve deleted by checking the Recycle Bin.
There are some other DOS utilities you can use to recover deleted files, but they are less reliable. One of the Utilities program i will recommend is Norton.

Another powerful utility program one can use can be download at
www.quetek.com

What does it mean if i suddenly stop hearing the power supply whir?

Without a cooling fan, Your PC can overheat very rapidly and expensive components can be rendered completely inoperable. if you suspect the fan have stopped working, try this
1.. shut down the PC Immediately. Allow it to cool for at least 30 mins
2. Apply power to the PC and Put your hand over the poer supply exhaust at the back of the case.
if you feel air blowing on your hand, everything is fine, otherwise replace the power supply