Bose with Partial Function
 

I introduced myself as a new-to-me Caddy owner a few days ago. Thanks for welcoming me, and all the tips so far! Here's my first tech challenge:

This 2002 STS has the single CD/cassette Bose and it does not work. The car had a bad battery, runs down to zero if left for a few days. Not saying there isn't an abnormal drain somewhere, but the battery really is bad. It charges, but doesn't hold well, and the case shows signs of swelling. Replacing it soon. The chimes work, but the Bose does not react to the "power on" button. The clock is flashing, and at night you can see that the unit's background lighting flashes too, but in opposing sync with the clock. Clock setting procedure does not work, but the random time it displays advances normally. I originally thought (as I pondered the purchase) it was a Theftlock activation caused by low voltage. But after reading about these systems, I know that "LOC" should be displayed if Theftlock is indeed active. I tried the generic GM Theftlock code retrieval button sequence, just in case the Seville is different. No reaction at all - still a flashing clock. I have tried all these things both with key "on" with the best battery charge I've had, plus with the engine running and battery voltage showing about 14V with the alternator feeding. I gather the chimes pass through the sound system in some fashion on these cars. So some degree of functionality seems to exist. Any ideas?