This often happens after a patch, and does not necessarily represent an actual error or need to repair the files. Most times all you need to do is close and re-open the launcher once or twice and the Play prompt will appear following which you can log in to the game.
I hope this advice will prevent too many people going through the rigmarole of checking and re-installing a whole load of files unnecessarily. Clearly there may still be occasions when the Repair prompt will need to be followed, but it's more often a fault with the launcher and closing and re-opening it will fix it. Usually the false reports and prompts go away a few days after patching.