FOUND A FIX!!!!! Hi Everyone, I just experienced the same thing: my Samsung Galaxy Note 3 was dropped and the LCD stopped working. However, the phone would turn on. I could not receive calls or call out. My USB Debugging was turned off. This is how I managed to retrieve my TEXTS, other Rooted info and normal files. I am not sure if the front end of this fix had much to do with the over-all fix, but it seemed to.
I turned my phone on. I pressed my "Volume Up" button until I heard it beep. While still pressing the volume button, I pressed the "Bottom Face" button, then my "On/Off" button. Pressing them all down at the same time, but in that order. This seemed to put the phone in recovery mode.
I went to this website and downloaded Kies 3 software from Samsung (free). http://www.mobile-phone-transfer.com/extract-data-from-kies-backup-sbu-file.html
I opened the software and then plugged my Old phone in. DO NOT plug your phone in until the program is opened. Choose the files you want to backup and then press the backup button (may be called something else, but you get my point)
Once the backup is complete, plug your new phone in and restore all of the selected files (you may choose which ones) onto your new phone.
It worked with no worries about the "USB Debugging" being turned on or off!!!!!!!!!!!!!Yahooooooooo.
I wanted to share this as not other option worked for me. Good luck!