I don't think you've destroyed anything...certainly not your motors, anyway (pretty much the only way to fry a brushless motor, other than by factory defect, is to overheat it).
I might have read this wrong, but are you running a LiPo cut-off with NiMH? If you are, then that would certainly explain the starting and stopping, but wouldn't explain why the B44 won't run without a Lipo cut-off...
...which might point to the sensor cable between motor and ESC. This sounds a little like a bad soldering joint perhaps on the ESC's sensor plug, but to have bad joints on the plugs of *both* ESCs is unlikely. Bad solder joints on the motor power wires would more likely cause cogging than random failures, so I don't think it's that. Which, in turn, might point to a problem with an item that's common with both buggies.
This is a strange one, but maybe i'm missing something obvious; I'll have a think. What actual NiMH cells are you using?
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