Computer Won't Start.

Alright, when I was playing some cs:go, my computer froze. After that I turned it back on and went on to go back to my match. However, it froze again. This happened to my comp some times, but it would work fine after I start my computer again. However, this time, when I press my power button, the lights, light up, but it doesn't go into windows. It just stays black. Another weird thing is that the fan spins, then doesn't, spins, doesn't, in that cycle. It feels like its clogged or something but I'm not too sure. Or maybe a computer part broke. Someone please help me on what to do because I cleaned the interior of my computer after and still didn't work since it sounded like my fan is clogged with dust, but I don't think it is. Would appreciate if someone told me what to do. :D