I've had problems like this recently. What you need to do to get the computer to actually turn back on is to either flip the power switch on the PSU or just unplug it for about ten seconds. Flipping the switch again or pluging in the cord again and hitting the power button should have the computer turn back on. If not, I would suggest testing other components in your build such as a video card.
If you would like a more accurate diagnosis, I find that some of the smaller PC shops spend more time on each computer because they want to figure out the problem so that their customers come back and refer their friends and family to go there.