BikingBrian,
Listening to your story, I would spend a few minutes verifying the integrity of your antenna system, and specifically the connector end in your home. If I understood your troubleshoot results correctly, your handheld works nominally with the rubber duck, and displays noisy performance on your outside antenna. Sorry to hear about your loss, but the bad guys probably didn't disconnect your old radio with any care for the connector. Throw that antenna on an SWR meter with your handheld as a source, and check SWR. You'll want to flex the coax a bit near the connector while checking SWR, looking for variations in the SWR value. You may find that your connector needs to be re-installed on your coax.
Pat-KA6P