Try deleting all of the files in the '..\Divine Divinity\Run\Dynamic' folder. Then re-boot (amazing how many weird glitches that can get rid of), shut down all non-essential programs, fire up Divinity, start a new game and see if hotkeys/right clicking work. If so, check your latest save again.
This folder is used as a cache for the game. Files are created / copied there from the save game folder when you load, and written / copied from that folder when you save a game. The files will be re-created as required the next time you start the game. If there was a corrupt file in that folder, deleting the files should fix the problem.
After this, if a new game works but your main one doesn't, there may be something wrong with the saved game folder itself. If neither work, there could be a problem with the game, in which case re-installing might help.
Zip or otherwise backup your saved games folder to another location first, just in case. Then un-install, re-boot, shut down all non essential programs (especially anti-virus), re-install the game, perhaps start the game and see if the problem persists (usually not necessary, but would help identify problems cause by the patch), re-boot, shut down all non essential programs, install the patch, re-boot, shut down all non essential programs, start the game. This procedure is a bit over-cautious, but the best way to avoid install problems.