Can't fix your alarm system, but I do have one valuable piece of advice. Never, never, never ever disconnect the battery while the car is running. The battery acts as something of a filter for voltage spikes in the electrical system. On some cars disconnecting the battery can destroy enough electronics to render the car unusable and cost several thousand dollars to repair. Sounds like you're OK, but don't do it again. For that matter, it doesn't prove much of anything about the alternator/charging system either.