I recently damaged my Blackberry 8700c. Looks like there's a glass screen behind the front screen. It was shattered. So I found someone selling the same model for $50 on craigslist. Bought it right away and it was really taken care of, looks like new. Problem is the the owner worked for a big bank and was given to him by his job. So certain things are locked and he doesn't know how to unlock them. I managed to back up my old BB, so I have everything on my computer to go into the new one. Is there a way I could just clean out everything on the new one, and then reinstall everything?

You will probably want to wipe the device first:

How to wipe the OS from a BlackBerry device? - BlackBerryFAQ

Then (as he was probably connected to a BES) perform the following:

Remove IT Policy - BlackBerryFAQ

So after I do this how do I reinstall the OS? After I backed it up I saw the applications were all that was backed up (sms, calendar, etc) not the OS (internet, etc.)

Check out the BlackberryFAQ, you'll find most of your answers there.

Details on how to upgrade the OS can be found here:

How do I upgrade the OS on my BlackBerry?