I gather you have a turntable with built in preamp. So the problem could be the cartridge or the preamp. You say the turntable has a balance control which does not work, so likely there is something wrong with the preamp.
What is your turntable, and can you find a link to a circuit for it and or a service manual?
If the preamp is at fault which I suspect, then you best bet is to take the output from the arm to another external preamp. If the unit is old and no circuit is available it may be hard to fix this, without purchasing an external preamp.