[Q] Any way to transfer data from an old Moto X with a broken screen and digitizer? topic

I dropped my phone, and
1) the digitizer, LCD, and glass are all broken.
2) I am not rooted or with an unlocked bootloader
3) I do not have USB debugging activated
I purchased a new Moto x (1st gen) and is there anyway, either directly or through a computer to back up my contacts, sms, data, and the like?