How to take a backup of a Moto G?

[Kaustav Mehta]

Hey guys!

 

So I went out the other day and bumped my Moto G (1st Gen) on the side of a table or something and when I came back the display doesn't seem to work. But here's the weird part:- When I bootup, the display works perfectly fine... Until the end splash screen, after which it becomes black. I know the phone still works as it does ring to incoming calls. Even the FastBoot works fine (Holding down Vol- and Power). But the touch screen is janky.

 

But it's gonna cost a hefty amount to have the display replaced by Motorola as its warranty is kinda over. So I'm thinking of getting a Droid Turbo or something along the lines( because dem 3 days of battery :3).

 

So my question is that, how do I take a full backup of my data from the phone considering the display doesn't work? Whenever I plugged in my phone to my computer a pop-up shows up on the phone asking whether to charge or use USB Data Connectivity. So is there a way to bypass this and just take a full on backup using some software?