I had the Binding of Isaac Rebirth on my computer bought off steam, and I had to switch accounts. Now I still have but I can't play or open it without buying it a second time. Is there any way I can play the games from my other account without having to repurchase them?
Assuming by "switch accounts" you mean Steam accounts, the game you purchased is licensed to you through the steam client.
When you launch Steam while logged in to the new account, it searches your hard drive for installed games to build the list that it shows you when you click "library". When you try to play Binding of Isaac, the Steam client then checks your user account to see if it is licensed to play that game. Since you switched accounts, your new account is not registered to play that game, as it was purchased on the other account. The game is installed on your hard drive, so it shows up in the "library" list, but the steam account you switched to isn't authorized to play it.
You can either switch back to the account that purchased the game (if possible) or you can re-purchase it on the new account. If this happened in error (you were logged into the wrong account when you bought it or something similar) you can contact steam support and they may be able to transfer ownership of the game from one account to the other, but you'll need to prove that you purchased it originally (I.E. you own the original purchasing account). If the game was recently purchased you could log into the old account and refund it, then re-purchase it on the new account (all this assumes that you have access to the old account still, of course.)