I've been having issues the last 2 weeks with 2005 mdx battery draining. First it was a couple of days, then it was overnight. I disconnected the hands-free module, but it didn't help. Now something is shorted out - The battery charger will not charge when the battery is hooked up, but charges fine when it's disconnected from the car (the battery was new as of nov 2019). I'm thinking it's the alternator? I'm at 250K miles, and it's the original.