There are a number of solutions to this problem. Unfortunately, troubleshooting this seems to be the most difficult, since there are many things which could be preventing the system from starting. Here's a list to get you started.

(NB: If your system is completely failing to give any power whatsoever, as in, "absolutely nothing is spinning up," pay special attention to the power supply and motherboard troubleshooting steps.)

It is important to remember that parts, more often than not, fail individually. Therefore, once you find a bum part, you're probably done. However, I strongly encourage you to follow all the steps of this troubleshooter, just to be on the safe side.

Before we begin, keep in mind that opening the case may void your warranty if you purchased a prebuilt system. You should only do this if you're comfortable with the idea of opening your computer and poking around in there. If the idea scares you, don't do it. If you feel like you have no idea what's going on, but want to learn, go ahead, but, again, be aware that you're voiding any warranty that came with the computer as a whole.

Most importantly, however, I must disclaim any responsibility for whatever happens to your computer. This is a detailed guide that had input from many in the Orbiting HQ, but if you screw up, I, nor anyone else at Ars Technica, can be held responsible. You are the sole person on the face of our mother Earth who can be responsible for doing anything, be it good or bad, to your computer.

1. Make sure everything is plugged in correctly