Power Supply failure
This is one of the most common hardware problems contributing to computer failure!
It's simple to diagnose....your computer doesn't work properly. (Was that helpful?)
Actually, it is a bit more complicated than that. Your power supply basically, well, supplies power! Sometimes it gets old or develops a fault, but still gives out some voltage....except that your computer may not start or only "see" half the memory you just installed, because it doesn't deliver enough power to run everything properly. It's a bit like trying to run an aeroplane engine on ordinary 91 octane fuel.
The best solution is to get a new power supply and install it. This is pretty easy, as connections are very straightforward. The main problem is getting a new supply that is up to the task!
The worst thing you can do is try to open up the PSU (Power Supply Unit) and see what is wrong...because even after power has been switched off, capacitors inside may store some pretty mean voltage.
There's a lot to look out for in a power supply, and getting the right one for your computer is essential. Depending on the age of your machine, it will have a different number of pins on the motherboard power connector....or even a different socket if it is REALLY old!
Use your old supply as a guide. Choose a replacement that has the same type of connector (and number of pins). Sometimes they have an extra block of four on them that can be plugged in if the socket allows it (see the example in the photograph).
Sometimes, your supply fails because you have added some extra components (memory, bigger graphics card, etc) and it can't deliver enough power to run it all. It's vital you choose one that delivers a greater Total Combined Output (TCO) than your old one. (Google the term) You should be able to find generic power supplies that don't cost the earth but deliver what they promise on the side label....not all do.
Installing them is a piece of cake, if you can use a screwdriver, but if you drop anything into the case GET IT OUT before you turn on the power...