I bought a game from the store, downloaded the game to my computer, and the game ran through steam. Then my computer crashed and eventually I got another computer. I logged into my steam account and it showed the game, but the game was in grey and i wasn't able to play.
Basically Steam doesn't know the game is installed any more. Just select Install from the game's page in your library and click Next Next Next... If you still have the files left over from the previous installation before your computer crashed then it will actually scan those files and validate them instead of downloading them again.. Otherwise it will just download a fresh installation so you can once again play.
You haven't installed the game in your new computer yet. Just select "Install" from the game's page in your library or double click the game's name in the list. This will open a new window that allows you to install the game. It works the exact same way as when you first installed it, just click "Next" and "Finish" a few times. This will install a fresh copy of the game that you can play. You probably won't have your old save files, so you'll have to start from the beginning.
The YouTube video below shows how to add money to Steam Wallet, buy a game on steam, download and install the game, and start playing the game.