Sims 4 won't start because of 'missing or damaged files'

This normally only occurs if your game package is misconfigured or corrupted therefore if the repair option does not work and you're sure that your save data is intact, you should contact an EA Game Advisor:

How to Contact an EA Game Advisor

You should also try renaming your "My Documents\Electronic Arts\The Sims 4" directory then re-launching your game to verify that it isn't data corruption or removal of files from your saves, however it isn't likely that this would cause the error you're receiving.