03 Lincoln Town Car FM radio has bad reception?

Our 2003 Lincoln Town Car is losing ALL functions but displays "phone" and operates the motor controlling the CD tray. Occasionally the radio spontaneously turns on and then stops again. The AM side seems not to work well when this happens. We installed a replacement and the same thing seems to happen. There's supposed to be a module in the trunk to control the radio but not in ours.

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