OK, I finally got around to taking everything apart and taking a look.
I discovered that one of the ICs on the circuit board attached to the motor (part 61 62 6 927 851 ) was completely smoked (You can even see burn marks on the cover):
The rest of the board looks intact and it is a waste to replace the whole thing because of a 75¢ chip.
Does anyone have a spare broken motor lying around that they want to get rid of?
Or, are there any electronics gurus that know where to source a few of these ICs so I can solder on a new one? Or maybe it is possible to cobble together some transistors that replicates the function of this IC?
The broken IC is a Freescale (Motorola) MC33286DW
[datasheet].