Tried it. I pressed as hard as I could but the button wouldn't go in
any farther.

Only one battery? If you have two or more, maybe your 1/2/both/off (or
similar) switch is set incorrectly? If you only have one, and some
stuff plays, maybe it's your ignition switch? Only other thing I can
think is that your ground wire is disconnected at the other end from
the battery, maybe at the engine/starter?