Computer hot and slow, is the fan broken?

[nano1000]

Hey, I just took my Macbook Pro out of it's case and it was really hot and was not logging in right (a probably unrelated problem that happens sometimes) and so I had to force it to shut down by holding down the power button, and when I started it up it was really slow, even when It was logged in, until now. I did not hear the fan running at all at any point, and when my fan runs I can defiantly hear it. Does this mean my computers fan it broken? If so what problems could it cause, are the problems I was having related, and is it replaceable?
Please help, and thank you.

 

[chscag]

If the fan stops or is not running in your MacBook Pro, the machine will shut itself off after a very short time. Go to iFixit: The free repair manual and look up the take apart instructions for your machine and check to see if your fan is clogged with dust and dirt.