Well I might as well add my 2 cents worth and also ask a question.I assume when you say it sets there idling with the sound still going that the light or lights on the front stay on in a continueouse mode and they are not flashing.?????
When it does that do you have control of any of the other features.?????
My experience with battery's is the tank just gets slower and slower when they start loosing power.Not saying it can't be the battery but they normally don't do that.The lights and what they are doing will help tell you whats going on and where.
The little guy on the motor is a "resistor" (thats my guess)but could always be wrong.(you said transistor) (wacky says capacitor)and I don't think it is either of those.It is what I call a draw down resistor and also used for a noise filter in a way and controls volt spikes.
One of the electrical gu-ru's will straighten us all out I hope.
I know everyone has there own opinion on charger's and battery's,mine being that I think those peak charger's just kill these stock battery's.And if you use the one that came with the tank it takes a long time to fully charge the battery. Good luck BIGMIG