Well, it's not entirely impossible but it's something like
https://www.youtube.com/watch?v=w2pf8iUgqqQ https://www.youtube.com/watch?v=TwvelNOHioY
What you'd need is a new digitizer but since it's one unit with the display, basically means replacing the display as a whole.
Alternatively you'd have to make do without touch and find some software hack instead to receive touch input from external source. But the only way for you to even install those is to modify the sd card directly since you won't be able to connect USB without tapping the connection confirmation dialog.
That's if you haven't already got an access path for telnet/ftp/modding.
I'd unplug the broken cable entirely just in case of any short-circuitry going on in that damaged portion.