Let's take a look at some of the possibilities.
If absolutely nothing happens when you press the power button, you almost certainly have a power problem. Electricity is not getting to the PC.
Unplug the power cord. Examine it for breaks or other damage. If you find damage, you know what to replace. Otherwise, plug everything back in, make sure all of the plugs are firmly in their sockets, and try again. (If the power cord is a laptop AC adaptor, check the connections between the different pieces.)
If it still doesn't work, plug something else—like a lamp—into the same socket. That will tell you if there's a problem with the surge protector or the electric outlet. If your surge protector or power strip is under your desk, check to make sure a wandering toe didn't turn it off.
If the cord appears to be fine and the socket works, try replacing the power cord or, in a laptop, the AC adapter. You may have to buy one specific to your model.
The problem could be with the power supply. If nothing else fixes the problem, consider replacing that. Desktop power supplies are usually cheap and easy to replace yourself.
That's not the case with laptops. Unless you're a very skilled technician, I recommend paying a professional to do the job.
If the PC starts, but fails before Windows can load, go into your PC's setup program, make sure that the hard drive is recognized and in the boot sequence. I went into details about this task only last month.
You might also consider booting with a live Linux disc or flash drive to see if you can access the contents of the drive.