OK, I might be late to the party, but if you still have this problem here are some ideas:

I believe you have a problem with the stepper drivers. Stepper motors usually don't break, so don't worry about that.

There are two possibilities that I can think of:
1) the actual stepper driver chip is defective. Stepper drivers are there as a link between a microprocessor and the stepper motor itself. The motor requires a lot of current, and is usually driven at a higher voltage too. The microprocessor can't provide this sort of current, and is usually run at 5V or 3.3V. So the stepper driver basically "translates" the low-voltage, low-power signals from the microprocessor to high-voltage signals, and can handle high currents. Some even handle the microstepping natively, so the microprocessor does not need to do that either. See if you can find the stepper driver chip on your scanners pcb, and replace that. The wires from the stepper motor should trace back directly to this chip, so if you follow those, you should find it rather quickly.

2) The power supply has a problem, and its voltage breaks down under certain load conditions. This is a little more tricky, since you need to figure out the type of power supply you have, and how it works, before you can start diagnosing the problem.
I had a similar problem with a laser cutter, which I managed to repair: it had a switching power supply, with 3 voltages: 48V, 12V and 5V. After testing all the components I could test (capacitors, resistors, fuses, etc) and replacing whatever I could, I finally replaced the controller chip, and the main mosfet transistor (which actually does the high-speed "on-off" switching), and that did the trick. I'm very sure it was the controller chip, but figured it would do no harm to replace the mosfet too, after ~20 years (the laser cutter is from '92)

If you can take some good photos of the PCBs, I might be able to help you identify the corresponding chips.

Greetings,

Oliver