Motorola Droid Turbo LCD cracked and computer won't recognize phone.

Last night I was hit by a car while riding my bike. The LCD cracked when I hit the ground and the phone is now not being recognized by my computer. I will hold the power button and the phone will make the boot vibration but after a while it will vibrate again. I am turning my phone in under warranty but I would like to know if there was anyway for me to recover my data. Any help would be greatly appreciated. Than you.