Printed aerials on windows are poor compared to the traditional wing or roof mounted whip type. Generally such things use an amplifier (booster) to increase the signal levels, a blown fuse would be the first thing I'd look for.
Not unknown for radios to go deaf, but the easiest way by far to check the situation is if you know somebody with the same make and model of car and swap radios. Fault moving or not tells a good deal..
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