Here is a link which describes how to test the stylus cartridge with an DMM (Digital Multimeter), using the Ohmmeter function. Try not to use an analogue meter (if you have one) as the current may be too high for the cartridge. This is for a Shure cartridge and may or not be applicable to what you have. You may have to check what brand of cartridge your unit uses and search for how to test it if tests totally different to what is described.
It may be that, if it tests faulty, that this is all that is wrong with it.
If it proves OK the wiring from the cartridge probably goes into some sort of pre-amp circuit before it is amplified by the main amplifier section. This is a representation of where the pre-amp sits in relation to the stylus and the amplifier, except in your case it will be built-in and not separate.
Unless there is obvious evidence of component failure, loose connections or dry joints, without a circuit diagram it may be difficult to determine where the actual problem lies. Tracing the signal path from the stylus through all the stages to the amp out to the speakers and testing the power supply rails is possibly the only way that you're going to find the problem.
Hopefully @OldTurkey03 will pick up on this and he may have a wiring diagram or service manual for your Audiotronics phonograph, as I cannot locate one.