Computer powers on but will not boot up.

Hello,

A few months back my emachine desktop computer of four years suddenly started acting up. It had a few blue screens and suddenly when I restarted it, it wouldn't come back on. When I press the power button the hard drive comes on like normally however, the light around the power button does not, nor will it boot up on the screen.

Every thing else works.

The screen comes on, the speakers work, the computer as far as I can tell works.
But the fan sounds like it's maybe going too fast or hard. It's really loud in other words. And when you try to turn it off by holding the power button down, it won't turn off.

You have to forcefully shut it down by unplugging it. Please help. I have some documents on there I would very much like to recover.

I have heard a myth that if you put the hardrive in the freezer that helps, but I'm hesitant to do so.