Really the only thing you can check is continuity from the connections in the head of the tonearm to the RCA connectors on the end of the lead.
There is nothing else inside the turntable that has any bearing on the question. Very unlikely to be a fault in the leads, but worth checking.
The answer is probably that the stylus suspension has lost all compliance. Playing records with it is probably not a great idea in this state. A replacement stylus might be expected to bring things back to as-new.
One would keep the pre-amp that was the better quality. Given both are pretty bottom of the pile, that isn’t an easy choice. As I wrote above, the turntable isn’t bottom of the pile quality, nor is the cartridge. They probably deserve a better pre-amp.
I’m curious why you would suggest replacing the stylus as opposed to the whole cartridge, which would eliminate many other failure possibilities all at once. A replacement stylus may not even be available for an old cartridge, and IIRC they’re aren’t exactly cheap relative to the cost of the whole cartridge.
The main body of a moving magnet cartridge just contains the coils. There is nothing to wear out. Stylus replacement is built into the design.
Shure cartridges are still supported and I would be surprised if there isn’t a compatible stylus available.
It just seems wasteful to replace the entire thing.
That said, the price will be a significant fraction of a new cartridge.
I get that. But bottom of the pile or not, I would still expect a pre-amp to produce a listenable sound. Neither of these do.
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No, but the arrow of blame is pointing to something other than the preamp to be the fault. Currently there less reason not to think that both are fine.
As I wrote earlier, I would have expected a weak but perceivable sound when not using a pre-amp and going in directly. That there wasn’t also suggests it is the cartridge. If the stylus suspension has hardened over time, this could be the problem. You might be able to judge this by eye. When playing the stylus will often have some noticeable motion relative to the body as it tracks minor warps or vibration coming from the floor. It it looks stiff, you probably have your problem. I’ve never seen one go stiff myself, but given the nature of its construction, I would worry about any old stylus. My turntable is down in the cellar where I put it when I moved into the house 24 years ago. It has a very nice and very expensive moving coil cartridge in it. I fear it may also be past its use by.
FWIW I’ve already ordered a new cartridge.
And now I check its tracking to learn that it is hung up in customs (it is coming from Canada).
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Turntables generally don’t have any “audio section”. They don’t output a line-level signal. The wires from the pickup are sent straight to the output jacks or cable, and must be fed into a dedicated “phonograph preamp”, or a receiver with a dedicated phonograph input that will amplify it appropriately.
Problem solved! The new cartridge did the trick. We are up and running and it sounds beautiful.
Thanks to all of you for your help!
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ETA: Spinning “Meet the Beatles” here.
I am curious. Did the cartridge have a mechanical or electrical problem.
Did the bad cartridge have a noticeable difference in the angle of the stylus beam compared to the new one?
Very glad to hear it! And speaking as a fellow turntable enthusiast and also as a Canadian who may have helped in some vague indirect way to manufacture or deliver your new cartridge, you’re welcome! 
I am not sure, but I did notice that the stylus on the old one was much less prominent than on the new. I am guessing it was a mechanical (worn out stylus?) issue.
I still have the old one, when I get a chance I’ll see if I can get a good close-up photo of the stylus.
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Hey, I have lots of Canadian blood in me (both parents, two siblings born there), so I will share some of that credit.
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