Our submersible pump stopped working so I replaced the pressure switch. I was very careful to wire the new switch the same as the old one, however the new switch blew a fuse when I turned the power on. I then thought I would try cleaning the points on the old switch with emery cloth and try it again. The old one also blew a fuse. Is there any other reason for blowing a fuse other than having the switch wired wrong? (When the pump originally stopped working it did not blow a fuse. Also, There was no pressure in the tank and the contact points were closed when the pump stopped working... if this helps diagnose the original problem).

Try with the pump disconnected.

http://www.catskillhouse.us/blog/wp-content/uploads/2007/12/well-pump-pressure-switch-wiring.jpg

This shows how it should be wired. Each set of points should have one wire from the breaker and one going to the pump.

Looks good, I would remove 1 wire to pump and try, then the other wire and try.
This will verify no short in the wiring, and pump is likely spent.
If you can access a means to rotate a little, turn power back on, then try again.