So my old TV speakers decided to stop working.

Is there any way to bypass the speakers?

The audio out jacks don't output sound either. Something must have gotten loose in the TV when transporting it.

Anyway, I'm using the coaxial cable from my wall for both analog video and sound signal. No cable box.

Is there a box of some sort that will connect to the wall's coaxial cable and then use the sound signal to my home stereo?

 

Got any old VCRs lying around?

Assuming you are using the TV's internal tuner, the answer is no. You'd need an external tuner (again, old VCRs work nicely, for this purpose, as do modern cable boxes) to pick out the audio feed from the one channel you wish to view among the dozens all coming down the pipe.