Proheat brushes won't work - belts are fine - ARRRRGGGHHH!!!

The direct answer to your question is: you don't. These machines are OK while they're working, but they are not easy to repair, and professional repair is likely to be uneconomical because of the labour involved. As to the cause: of course I don't know without seeing the machine, but I do know that the brush motor is located in a position where it quite easily gets wet and eventually fails (possibly causing damage to the machine's electronic circuit board as well).  My best advice: before you buy your 4th Bissell, read what you yourself have written...! And consider saving money by hiring a professional machine occasionally.
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If the brushes do not rotate when the power is on and the handle is leaned back , the brush motor as blown and the cicuit board . the brush motor is situated in the base of the machine and the circuit board in the lower handle , this is a job for a bissell engineer.