How to backup a broken iphone without a passcode?

Well i broke my iphone so the screen does not work. But if i plug it into my laptop then it still connects to itunes. I have important stuff on it that i need to transfer to my new iPhone but i can't back up the broken iPhone because i had a passcode on it and i need the passcode to back it up. Is there any way i can get all the information on the broken iphone onto the laptop? Do you think i could just go to the apple store and have them switch it?

Its a broken apple product… Sorry but I think your screwed