The warranty on these are not transferable. So no, you don't have a warranty.
Fully charge your battery before attempting to use it, otherwise you can damage it or decrease its longevity. Once your battery is fully charged and you have checked all connections, you should be OK. If you still have the problem, now it will be even easier to pinpoint since you eliminated the battery and the connections.
For your previous battery, a voltage of 11.5v means it was down to 20%. Here's a little breakdown...
12.6v or higher - Fully Charged
12.5v - 90%
12.42v - 80%
12.32v - 70%
12.2v - 60%
12.06v - 50%
11.9v - 40%
11.75v - 30%
11.58v - 20%
11.31v - 10%
10.5v - Bone Dead