I'm not a troubleshooting expert by any means, but I'd try getting the game to re-create its settings first. Always backup any files you're messing with of course, that way you can copy them back if something goes wrong.
PC2's settings and saves are in a Project Cars 2 folder in your Documents folder. It's not unheard of for issues to happen corrupting your controller profile or local settings which are in savegame/[long number that is your Steam ID]/project cars 2/profiles. Deleting those(or moving them somewhere else) causes the game to create new ones with defaults and has often fixed people's stubborn issues. I had to delete my controller settings myself to get my wheel working at one point.
For graphics issues I'd think it could be something wrong in the default.localsettings file, or perhaps in the very top level there are two xml files for graphicsconfig and triplescreensettings. I don't know for a fact those two would get rebuilt automatically but I wouldn't be surprised if they do. Like I said, just back them up somewhere else in case you still need them.
You can of course try verifying the game files through Steam, not sure that would touch any of the settings-related stuff though. There are still one or two people who hang out on the game's Steam discussion board that can be quite helpful. I've seen a number of people's issues resolved there. There's also the game's official forum at forum.projectcarsgame.com. It's closing at the end of the month though so if you want help there you should ask quickly.
If the game has never worked at all for you, it could mean something else is wrong too.
