If the tape deck is no longer working, the most likely explanation is that the tape deck switch is stuck in the on position. This is usually because the tape deck mechanism resets at the end of use and if the deck malfunctions (usually due to failed drive belts), the mechanism cannot reset leaving the switch on. That switch also controls the main amplifier which is necessary for tape operation which is why the boombox usually remains on.
Of course the other possibility is that the main power switch has failed but that is relatively rarer. It’s usually the other cause.