If it's 12v TM, temporarily disconnect the positive (red +) TM wire from the battery and put a 12v light of some sort between the positive terminal of the battery and the positive (red) wire to the trolling motor. DO NOT activate the motor. If the light's on with the motor off, the TM is drawing current. If it's off, it's not.
The battery may be sulfated... If this is the case, even with a full charge it will almost instantly run out of steam and this can happen to any battery unfortunately. Only way to be sure is to get it load tested - Any chain auto store should be able to do that either free or for a low fee.