The record and volume slider resistor boards are incompatible. The resistor values are too different: 50kΩ vs 500kΩ and the tonal curves are different too.
If you are hearing any sound coming from the L speaker, then the resistor board is most likely not broken or fractured. A more probably cause is the small internal feelers are loose or detached or there's dust and debris accumulated inside the sliders. You can try faderlube from Caig, flip board upside down while flushing the sliders and see if it helps. Turning the board upside down as you do this allows the chemical to drain out. Obviously this is much easier if the board is removed from the boombox. Do not overwork it and if it does not improve, the feelers might have become detached, in which case, stop and fix it. Continued movement might grind the loose feeler into the resistor track and degrade it.
If the feelers have become detached, then you'll have to disassemble them to repair. This is a rather delicate task and once you begin, you may have to repair the volume, bass and treble sliders too, as the audio signal goes through all 3 sliders before it makes it to the amplifier.
I still repair these, but only if they are virgin unmolested sliders, as I do not repair other people's work. Generally speaking, you can only open these up once or twice before the holding tabs the secure the metal case to the resistor board breaks off, so it's important that they be done right the first time. There are limitations to what can be repaired and customer pays all shipping charges if international.