650 service questions

I purchased a 2006 650 convertible last summer. Only 35,000 miles.   Occasionally when starting the car it sounded like maybe the battery was not strong enough.  I let the car sit over the winter and now the car will not start.  I did charge the battery and it ran at 1/2 power for about 2 minutes and then stopped.  I charged it up again and it will not catch now.  I talked to a BMW Service technician and they thought it probably was the battery.  I have not tried to jump the car yet with another vehicle, but it really turns over strong.  do you think the battery is the only issue?

thanks,

Jim