98 town and country lxi with factory infinity audio. Am, fm, cd, cassette. Everything works when the key is just on, if you crank the engine. Fm will only play static ( does not sound like any kind of transmission or weak signal, just static ). Radio will scan but not stop on any stations. If you turn the motor back off, you can tune stations in again. Less than 30 seconds, then it goes quiet again. Power cycle radio with power button. Stays quiet, power cycle with key. It will work again, but only briefly. The am will continue to operate through all of this. Could this just be an antenna issue, or should I be looking at the head unit.
Common problem in the radio that once fixed, it's fixed for life. I have replacement FM tuners but I know how to repair them now instead of replacing them. You provided a lot of nice detail but in this case I suspect those clues are coincidences.
These combo radios are built by Mitsubishi and are real high quality. I sell a lot of them for upgrades at the nation's second largest old car show swap meet.