I am an electronic technician, been fixing radios since 1981 for a living.

My bet: It is not the radio. There is more than one source of power to the radio, sounds like maybe a battery lead that SHOULD stay live is not staying live or a switched power lead is powering up and down quickly during startup, causing the power up process to "freeze".

As a side note: There is no dealership I know of equipped to fix a radio at the component level. This would take equipment and training that woulid simply not pay for itself unless you are working on radios for a living. That is not what auto dealership service departments do. In this case, getting a replacement radio that fast is impressive, you have a good dealer.

The only thign now, is finding a tech at the dealership that understands what is confusing the radio during it's power up process. Good luck with THAT, I hope Chrysler tech support is effective and can help the local people understand what to look for.