- Tips on diagnosing problems -

I get a variety of faults with computers but they fall into two main categories.
_Hardware_And_Software_

[ Hardware ]
The most common fault is when pressing the power switch and nothing happens.
This situation is most likely to be a power supply fault. Computers use a special type of power supply nearly always located where the Mains Power lead connects from the wall socket.
They all have a fan inside them for air circulation. As a result there will be a build-up of dust over a period of time. The dust inside the power supply (and also inside the Case itself) reduces the cooling and will cook a power supply.
I highly recommend cleaning out the computer with compressed air (or a reverse airflow vacuum cleaner).
The main fan inside the PC case is used to keep the CPU chip cool. If the heatsink where the fan is mounted gets clogged up this will cook the CPU. This has to be kept clean.
A hot CPU chip will cause the computer to shut down a short time after you turn on the PC.

[ Software ]
You are probably using Windows (98, 2000, XP or possibly Vista).
If you have a software fault it will either be a blue screen with a message of some type or you may be able to get as far as the Login Window (if you have multiple users).
The most common problem with Windows can usually be fixed with a rescue install of Windows. This will not overwrite you current settings. It just replaces all the Windows files with the originals from the installation disk.