When I've had this problem, it turned out to be a poor connection of the center conductor to the connector plug at the point where the antenna coax plugs into the radio. Any poor connection between the mast and the center conductor of the coax will give poor AM reception although the FM seems to work OK ( as long as you are near the FM station towers).
It's a pain to pull out the radio but I think you'll need to get at the antenna coax connector on the back of the radio. You can then look for a loose connection at the center conductor. Mine was visually obvious. You can also use an ohmmeter to measure the resistance from the center conductor at the radio to the mast which should be only a few ohms. If it is high, the connections are bad or there is a break in the coax (unlikely) of the coax connection to the antenna mast is faulty.
A thought comes to me that you can use an ohmmeter to check the resistance from the antenna mast to the car chassis. This should be a high resistance. If it isn't, then there is a short circuit somewhere in the antenna mast mount, the coax, or at the radio. I think I'd start with this check. If you don't have an ohmmeter, you can get a very inexpensive digital DVOM at Harbor Freight or Sears which will prove very handy in car work. They are easy to learn to use. Harbor Freight had some basic DVOMs on sale for under $3.00 so I put one in the trunk or glove compartment of all my vehicles.
Good luck.
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