Sounds like a bad ground - either at the radio or the antenna.
You can try and relocate the factory radio ground to another location - make sure its a chasis ground - not just any metal part under the dash. It may not hurt to relocate the 12V switched/ignition wire on the radio as well.
As far as the antenna goes - look for corrosion where the antenna is mounted on the under side of the fender (you may have to remove the antenna).
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Nelson
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