Can I retrieve data with a busted/unresponsive LCD?

My wife dropped her S6 edge a few months back and broke the back glass. Everything worked fine, though, until a few days ago when the screen suddenly stopped working. The screen displays two columns of alternating gray lines if the power button is held down for a few seconds or if the home button is pressed (picture showing this is at the bottom of my post); otherwise the buttons seem to be non-responsive. Also, the left-most LED is illuminated solid purple-white almost all the time (sometimes it flashes yellow and then goes back to purple-white). I brought it to a repair shop, and they said it was a broken LCD.

I'm trying to figure out if there's any way to get the data off the phone without dropping $300 to replace the LCD. It's not rooted, and USB debugging isn't enabled. Also, she already got a replacement phone and swapped out the SIM, for what that's worth. Basically, I only really care about the pictures of our kids, but she unfortunately didn't have Google photos sent to sync, either.

Additionally, neither Windows Explorer nor Samsung Smart Switch recognizes it when you plug it in. I've tried attaching it to both a mouse and a keyboard via OTG adaptor to try to unlock the pass code (numerical, not pattern). It doesn't seem like that worked, though, because nothing happened again after doing that and then plugging it into my computer. I was going to try the trick of hooking it up to my TV, but I've read that the S6 Edge doesn't support MHL, so that seems like a bust.

Any thoughts? Suggestions are most appreciated. Thanks!

(image of the screen) http://i65.tinypic.com/nqwxth.jpg