IPhone – Back up iPhone that can not be unlocked–screen is broken/shattered. Need help!

I left my phone on the roof of my car and drove away on a busy road. It was hit several times and the screen is broken/shattered and glass comes off of it. It receives calls/text messages, and the button on the top to turn on/off still works. The screen is just in such bad shape that it won't register the touch of my finger. I have an appt with Genius bar in a few hours to get a new phone. I want to save all my pictures and apps off this phone if possible (I never backed up on the computer prior to this) but it prompts me to unlock my phone and I can't do it. I can't use another iPhone as a guide, because it won't even recognize my finger touching the screen, but the phone still works. Can I get some ideas on how to back it up? I am not tech savvy and this is a difficult problem!