The Samsung devices that support the S Pen have two separate digitizers, one for fingers and the other for the S Pen. So it's entirely possible for one of them to fail while the other continues to work, as in your case. There's another thread on a Galaxy Note 10 full of people who are having the same problem as you, along with several suggestions and examples of things they've tried that have fixed their problem. Take a look and see if anything there helps.
[post|127695|Why does my tablet respond to S-Pen but not my fingers? - Samsung Galaxy Note 10.1 - iFixit|new_window=true]
Personally, given the condition of the screen, I'd be tempted to open it up and check the connectors going from the tablet to the display. Sounds like you've either got a bad connection or possibly a bad (or damaged) display.