Someone PLEASE help me! I need to back up my phone!

Hello everyone, im new on here. im sorry if this is the wrong section.

About a month ago my iphone 4 screen cracked so i went to a store and they fixed it, 5 days ago i dropped my phone. The screen stopped working it was COMPLETELY DEAD the screen is black! but it seems like the phone is still functioning properly when someone calls me it rings but i cant answer because the touch screen doesnt work anymore. I got a new phone today i want to back up my old iphone but i cant! everytime i try to back it up it says "iTunes could not back up the iPhone “Sarah's iPhone” because it is locked with a passcode. You must enter your passcode on the iPhone before it can be backed up."

I know what's the password but i cant enter it because my touch screen doesnt work anymore!!! I would do anything to back up my data! There are really important numbers on that iphone! what should i do?