Talk to the IT people at work, if they're willing to help they can explain how to back everything up. I'm guessing company policy wouldn't allow this but it can't hurt to ask.
Keep in mind they may not consider anything on a work computer to be "personal", but as was already said, it doesn't hurt to ask.I am currently using exchange at work. I will be quitting this job and I want to be sure that my personal contacts and email are not lost/deleted.
Thanks