iPhone crushed in Lost mode. Charges but won’t connect to itunes

If the digitizer is broken, then you will need a new display. Looking at iFixit prices, they are $95, 85 if you send your old screen to iFixit. This screen is a lower quality (there is an image showing the difference) one than the one that came on your iPhone, but since you are just trying to recover the data, you don't need awesome colors or resolution. On to the replacement! Just follow this guide to replace the screen. Also, once you recover the data and factory reset the phone, you might want to consider trying to sell it on eBay or some similar vendor, depending on how thrashed up the phone is. Even then, you may be able to sell it "for parts only". Just make sure you specify that the screen is a lower quality LCD.

Good luck!