New 1999 Cadillac Deville owner

I love this car! Is in good shape. I've always been a Ford girl, but the price was right and the test drive was outstanding. We are just having one problem, though. They still had the factory cassette radio in the car and we had it changed. Sometimes the car alarm continues to go off and car won't start. Is it a good idea to mount the original factory radio in the trunk? We had a specialty shop install the radio, but after a month the car has also gone into sleep mode. Thanks for any advice.