Yes, it might be possible to modify the board with fixed resistors instead. But the curve might not be linear so the slider will need to be disassembled to determine what the values should be when the slider is in the middle position anyhow. You should know that the other sliders (bass/treble/record-levelsX2) are similarly constructed and probably not far behind. OR they might already be bad too, The design of this boombox is such that a bad bass or treble slider (they are both stereo controls as well) will also cut the sound to that channel. On most others, a bad bass slider translates to non-adjustable bass. On this one, it transalates to no-audio-signal pass through. Of course there might also be an issue with the power amps as well but first things first, I know for a fact that a balance slider missing it's feelers will result in no audio in the channel with the lost feelers. Just trying to tell you from experience that it's not uncommon for multiple issues to exist and with NO audio right now, there is no way to know for sure until you resolve it one issue at a time.
But before you go any further, you need to determine if the preamp is working properly. See if the boombox will output a normal signal from the line-out jacks which is fore of the tonal controls. If yes, then I'm pretty sure the issue is in that tonal board.