How to get data from a phone with a broken screen and USB connection lock

[Screencracked]

No cracks or any cosmetic damage, phone did a 'cracking' sound while was laying on a table, no physical contact, and seems something went wrong inside.

As a result, the screen is black and does not turn on, I hear all sounds, facebook notifications etc.i, sometimes couple pixels pop in a corner, sometimes I manage it to unlock (sound), so touch not dead entirely.

I want to extract all data before opening it, but... I have turned option "Ask me permission to use the phone as storage when connected to PC"... what a failer =(

Tried to run recovery tool, no go. I'm out of moves right now, any suggestion, please?

 

[Guytronic]

Welcome to WC!

What kind of data needs to be extracted from the phone.
Anything in One Note, Word, Excel and pictures can be recovered via a backed up Microsoft account.
Most apps such as Dropbox/Box or other cloud stuff can be logged into via desktop.

If it's messages or contacts those items will also be saved to cloud services and they should reappear by signing in with the current MS account on any other Windows based phone.
Good luck there and do join us here as member if you would like to.

 

[Screencracked]

Well, let me make this task more complicated. Last couple months none of the content backed up to OneDrive. Why? Cuz drive was 9.5/5GB (MS reduced cloud space and I didn't notice.

Now I removed everything with a hope that phone will start sync, but... nothing. Probably "sync only while wifi on" is ON and phone sitting with only LTE enabled =(

Can I manually force a sync and then wipe the phone?