CPU Problem?

My computer powers on, (case lights/fans turn on, cpu fan spins, harddrive makes sounds) but doesn't boot (my usb mouse doesn't light up, monitor doesn't recieve signal). However, when I press down on my cpu fan, pushing it towards the mobo gently, it works.

But then, the computer freezes up after about 20 or 30 minutes randomly.

Any ideas?

Sorry if I missed something I'm a first time poster.

Sounds like the CPU fan needs to be replaced. My guess is that the fan speed isn't being read by the BIOS correctly until you touch it. I would try a different cooler and see what happens. Sometimes when a certain BIOS cannot monitor the correct fan speed it will not allow the system to boot.

but how does that explain the random freezing?

Again, your BIOS might not be reading the correct fan speed thus causing the system to freeze up. Some BIOS require a proper fan speed to be recorded in order to remain stable. The fan you're using might just be slightly out of par. To debunk this theory, try a different cooler. If the same thing happens, then the problem exists elsewhere.