I tried to to play Skyrim today and Steam told me that it needed to install an update first, something about a more up-to-date version of the game?
It was unable to install the update (I can't remember the error message) and now I'm unable to play the game.

There is now no "Play" button in the Steam client, only an "Install" button. I already restarted my computer and that didn't fix the problem.
I also can't right-click the game and "Verify the integrity of the game cache" as the option is grey and un-clickable because it thinks the game isn't installed.

I checked the files where it's installed and they're all still there, so I'm not sure what to do. I don't want to have to re-install the game because of all the special mods I have, so is there some little simple thing I'm missing? I've searched several times for solutions and most of them say to verify the cache, which I'm unable to do since Steam doesn't even think the game's installed.

Thanks in advance for any help, it's greatly appreciated!