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.
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!
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...