@MikeInNH. My 1966 Rambler had a transistor radio which was installed at the factory. My dad had a 1963 Studebaker Lark he purchased as a new car and it came with a transistor radio. I believe tube type radios were gone by 1962.
The 1960 Rambler my parents owned had a radio that had tubes, but the plate voltage on the tubes was 12 volts, so it didn’t need a vibrator, transformer, or rectifier tube.
In the case of the OP, the problem seems to be in the RF section of the radio. If the antenna is good and adjusting the trimmer doesn’t help, I would look for a blown transistor in the RF section.
If the radio is just an AM radio, it would probably cost less to buy a new after market radio than repair the present radio.