The monitor won't come on either and the CPU fan isn't running.
This same thing happened to me at work.
After installing a new computer and setting everything up, I left thinking I was done.
A week later, the coworker who was using it called to report the same sysmptoms you have reported. I went over and spent the next two hours trying every convoluted method I knew to coax the machine back to life.
In a fit of frustration, I went to disconnect the whole lot and take it back to my office for further work. As I knelt down to take the power cords out of the surge protector, I noticed that the switch of the protector was off.
The lesson: Make sure it's plugged in!