Thanks to Fraser's sharing of his experience, the toothbrush is now working excellently after I soldered the connections to the battery (the new battery's tabs onto the tabs left behind from the previous battery). The toothbrush can now, with one full charge, deliver 22 sessions of brushing with an average brushing duration of 2 minutes and 45 seconds per session. Even after the 22nd session, the toothbrush didn't stop dead, but I decided to recharge it at that point because the motor became noticeably less vigorous. Prior to the new battery, the motor would just stop dead in the midst of the 5th session.