Power issues

I am a Hp pavilion a250n which has an power issue. Heres what happened. I was playing a game when a blue screen came up with a high pitch sound coming from the computer. When I turned off the computer and turned it back on there was no picture coming on the screen. So I turned off the computer off and repeat the process. Still no picture. So I turned off the computer and unpluged the computer from the power supply. I plug it back in and the same problem came up again meaning it will not boot. I did that same process back over. But when I plug the computer back in the power supply the computer did not come on. I push the power button many times and even unpluged it and pluged it back in. Nothing. I even tryed different power supplys.Nothing. But i did notice one thing, When I wiggle the connecter plugin from the computer to the power supply, the power supply trys to power on but it acts like the power supply don't gets enough power. But the power is not the problem. May you help me with this problem. I even went on the Hp website and the tryed their troubleshooting tips. Also it did not work.

P.S. This is my second computer that has the same problem. Will not power on.