Wow, 2 years ago? You must have not been using it for that time if the digitizer was broken.
It sounds more like a hardware problem with either the new digitizer, or connection to the motherboard. Hard to say really. I've never replaced a screen, but is it possible to remove/reseat the digitizer connector without pulling the new screen off? If so, you might try that.
As far as backing up you data to your PC, you would need to download and install the Samsung USB driver...
Technical Documentation | SAMSUNG Developers
You could also install Kies to see if it can talk to your phone and back it up...
Kies