2004 BMW Z4 Battery/Alternator

I only drive this car for leisure and in the summer. The battery went dead over the winter but I charged it fully with an electric charger and then put a battery tender on it for the rest of the winter.

It started and ran fine, but the second day I drove it, it didn't start again. I recharged it, it started and then after sitting for several hours almost didn't start again. The battery indicator on the dash renders a low signal and then goes to almost halfway after running for awhile.

Would the cause of this be a poor battery, alternator or both? And being that it is still under warranty, would this be something that would be covered if I called the dealer?