The game doesn't need compatibility mode. The game not starting at all (as opposed to starting then crashing) is a Steam problem.
Here some things you can try:
- Turn off your antivirus. It seems it can interfere with Steam sometimes. If the game runs, try turning it back on.
- Turn off Steam Cloud synchronization for The Quest: Right click on the name of the game in your Steam Library, select Properties, then the Updates tab. The checkbox is at the bottom.
- Delete, then redownload the game: To delete it, right click on the game, then select Delete Local Content.
There might be other causes, but I'm not that knowledgable in Steam troubleshooting, sorry.