Step one: get an extension cord and plug the computer into an outlet far away from the one you are now using. With luck, the problem will be the outlet, not the computer.

Be sure to use an extension cord which is at least as thick as the computer's own cord, if not thicker. This is in keeping with the safety principle that you don't plug a thick cord into a thin one.
=========
Meanwhile, back up any treasured data you have before the puder goes belly up.
========
I used to have a computer with a very touchy ON button. The shop gave me a new power supply, and that fixed it. It turns out that the 'power supply' is not the local electric company (as I thought) but part of the computer. Your problem might be in your power supply.