I've been working on a Taotao 125 starting issue. Originally, I got it and it would not start, but the solenoid would click. I tried jumping the solenoid and nothing happened. I assumed it is the starter. Used multimeter to test, and I was getting almost 14 volts at the pole on the starter. I took the starter off, took it apart and plenty of plastic fell out and you can tell it had melted. (I'm not sure what a good one looks like, but definitely melted plastic inside) So I dumped everything out and put it back on just to see if all the pieces were keeping it from moving. Now I do not even get a click on the solenoid. I checked again and still have 12+ volts going to the positive side of the solenoid. Did the bad starter fry the solenoid now too?

 

Probably, if the contacts on a solenoid get hot they can "weld" themselves together. Luckily, both starters and solenoids are cheap for these machines.