In Star Wars the arcade game what happens if you choose not to blow up the Death Star?

Somewhere… I have a book that would tell me.

But there is Wikipedia, which says that if you fail to hit the exhaust port, you lose one shield (or are destroyed if that was the last hit you could take), and then have to try another trench run, where if you again fail you’ll lose another shield, etc.

So no, the Death Star wouldn’t blow up the rebel base, but you’d die and lose that way. (And then one might assume the Death Star would blow up the rebel base after you’re dead, unless some other Rebel managed to do it after you died.)