Hello,
I have the same problem with my Samsung Galaxy S3. Screen doesn't show anything, but phone powers on and off. Can't unlock it since touch screen doesn't work and can't enable USB debugging.
Tried several things such as SmartSwitch, DrFone Wondershare, Wondershare Mobile Transfer, but all of them require USB debugging or they fail for other reasons.
My main goal is to transfer all of my data to a replacement Galaxy S3 (not a brand new one), but I'm not sure what to do exactly at this point.
The only thing I can think of is replacing the mother board onto the new S3, then saving the data using that phone and perhaps putting the old motherboard back after and restoring the backup onto it. Is this my only option, or can I do something else? (Excluding purchasing a new screen)