This is the first report of a controls problem. Unfortunately the controls don't have much code in them so I don't know of any change or failsafe that I think could help.
The basic troubleshooting I can suggest is:
1. Try restarting your computer
2. Check to see if you have any game pads plugged in
3. Check to see if the full version of the game has fewer files than the demo version
If you are still unable to get the full version to read your keyboard inputs then ask Itchio for a refund and I'll approve it.