2013 Base Cooper, 650 miles. Went to work on Thursday, locked up the car and noticed the rear lights were still on. Weird, yep car is off and locked, front lights are off but rear lights were still on. So I turned off the auto headlights. Leaving work I hop in my car and get the symbol for remote control malfunctioning or not detected. I did have a bag of books (work at the Library), so I just moved my bag and the car did start. When I got home I could not lock the car using the button on the handle. After fumbling around my books I finally located my fob and hit the lock button and the car locked. I bought a new battery just in case, but the car only has 650 miles on it, I wouldn't think it needed replaced. Any opinions if it is the battery or the remote failing?

Thanks!!