Nearly everything fried at one time or another in the scooter controller (wasn't a wheelchair, was just a crappy sit-down scooter; not sure I have a pic but I'll edit it in if I find one; was a LONG time ago). I had to do PCB repairs at least once to make it work; the FETs got moved outside the case (onto that heatsink in the posted pic) partly for heat and partly cuz they were so big they wouldn't have fit in the case.
Eventually I tried learning to build my own, and ended up with a 2QD (from 4QD.co.uk) PCB that I then built up from scrap parts and used for various motors on this and other bikes, and blew up repeatedly, but not as badly as the cheap scooter one. There's some info / pics / etc on the old blog
The Electricle™ : Bicycle Electric-Motor-Assist Project from before I found this forum. Eventually I ended up with a Curtis golf-cart controller, before I finally went brushless hubmotors (because at this point the systems had so much torque that any derailment of the chain drives they were running destroyed too many bike parts--sprockets, chains, wheels, even my CrazyBike2's frame was being bent. (there's a long thread for that one's development)
Which two pins on the "transistor"? If it's a FET, there's a gate, source, and drain. Shorting S and D is like shorting across a switch; those are the two current-carrying pins. Gate is a tiny switch to turn the big one on, and shorting it to one of the other pins has different consequences depending on circuit design and which pin, etc. Can blow up the FETs doing that, too, and the gate driver (sometimes a chip, sometimes the MCU, sometimes a transistor).
On a brushed controller, shorting across S&D would run the motor until you take the short away, for a typical half-bridge 1quadrant cheap brushed design. A full bridge design would only run it if you shorted across both FETs, or one was already blown shorted on (most common failure mode of FETs) and you shorted the other.
