So.. I have a portable radio that broke. My little brother put the batteries in backwards. There was a bad smell and the back was hot. I took them out and It worked. Sort of. There is no sound. I only tested in FM mode. Any idea how to fix this? Radio is Tecsun brand, model PL-606.
 

Which batteries it used? Alkaline or Zinc-Carbon? I've never know that if you put batteries backward, this destroys the entire product.

You would need to disassemble it and look into the electronics.

Most likely the audio output amplifier will be toast, as that uses to run direftly from the battery voltage. Plus can not tolerate any resistance or so in series with the supply, so nothing to protect it.
The rest will be behind some regulators, so there just the regulator ICs may be damaged. Plus it is likely these will be separated by some resistors or filters, so rather high chance the regulators will survive.
Fortunatelly both the amplifier, as well as regulators are rather common components.

And I don't think there would be anything damaged in the main signal path, where the main proprietary parts are.


Edit: I just looked into PL310  schematic, which seem to correspond to the same description as published in PL606 manual (mainly using the same SI4734 DSP radio IC) where practically the whole radio is behind a transistor power switch, only the processor is supplied all the time

So I see rather high chance for it to be fixable...

Don't touch it unless you're experienced in soldering on circuit boards, or you risk making it even more broken. Desoldering is harder than soldering, if you aren't careful you can lift traces.

Tecsuns aren't really cheap, so you might want to take it to someone who actually has the experience.