Wow, that's a bit of an off brand...
It may be hard to find parts for.
If you can find parts, replacing the board with the audio section on it will be the easiest fix.
The cheapest fix is to get a stereo potentiometer, and put it inline with the speaker so that you at least have a manual volume.
If you are capable of running the unit into a stereo, see if the mute button works, the mute usually won't affect the line out, and you can control the audio from your stereo.
Here's a (quick and dirty) schematic of how to put a potentiometer in a speaker line correctly.
The idea is you can control the speaker anywhere from leads shorted (no sound) to leads across tv output (full volume). Choose a potentiometer value around 100 ohms with a linear taper if you can find it. Most pots will be logarithmic..for the most part it won't matter.