In my case, it's the factory issued cassette deck (CR-915, I think). It's key inputs are not working, only the power switch - at which point I'm prompted to enter a code which doesn't register due to the failed keys. I did take the time to open it up, and see if there was a cold solder joint, burnt component, or other visible sign of failure. My eyes (and nose) could not detect any. Great suggestion, however. My very first VCR (maybe my only one) was given to me non-working. Having no idea what I was doing, I somehow thought to adjust the heads (after cleaning them) while the thing was playing a tape, and got it working fine. When something's already broken, there's nothing to lose, as you point out.

Incidentally, I can personally live without a sound system. Having something in the car which doesn't work bothers me more. But I also have young kids, and they benefit from some tunes. Just like the OP, I listen to podcasts, but I'm happy to use ear buds for that - one of the more heinous crimes I commit on a regular basis...