If your computer is not powering on, you may just have a defective power button.

To test the power button:

1. Start by unplugging the power switch from your motherboard.

2.  Take a flat head screw driver and touch it to the two pins the power switch was plugged into for 1-2 seconds. 

If the unit comes on then the power button is faulty, otherwise you may want to try the paper clip test on your power supply.

The majority motherboards have the front panel pins configured  as in the diagram below. If your front panel appears like the one below, in step 2 you will be touching the tip of the screwdriver simultaneously to pins 6 and 8 of the diagram.