Computer powering up but not booting up.

So I was having a problem running most games. My computer would run it fine. But then after about 5-10 minutes it would turn off. The PC would still be running. But the screen and the audio would be off. I was told that this is because of a faulty power supply. So I bought a new one and installed it and it was working fine until it did the exact same thing as the old one. And turned off mid-game. After this I thought it was because of dust that was gathering in the cpu fan. So I cleaned it out. Also I took the cpu out and put it back in (I don't know whether I should have done that). Then I took the graphics card out and put it back in. Now whenever I power my PC on. All of the fans spin and all of the lights turn on but the computer does not boot up. I just want to know if anybody knows what the problem is and if I can fix it?