I would like to disagree that it is illegal or unethical to open up V5 motors for servicing (like lubrication) or swapping out identical, VEX legal, parts between two defunct motors to make one working unit.
We could guess with high confidence that the reason GDC put that text in the Game Manual was to address the issue of some teams cheating by shoring out overcurrent protection PTCs in the old 393 motors. And that they issued a blanket “no modification” rule because they didn’t want to go into a rabbit hole of interpreting “no modification that gives you unfair competitive advantage” language.
As they like to say VRC ethos is about learning STEM without cheating. And the fair repair, by swapping out VRC legal components, perfectly fits such mission of learning, without violating the spirit of no cheating.
The only advantage you gain by repairing your own motors and learning how they work and fail would be that you will become a better engineer.
I guess, you are talking about the components in the top left part of the motor PCB:
And, as @sazrocks said, those are likely ferrite beads connected like in this diagram (source) to supress EMI noise from the brush/commutator contact bounce of the DC motor.
If you suspect that FB2 acted more like a “Fuse Block” than a “Ferrite Bead” you can, first, unplug the DC motor from PCB and then try to spin it by hand.
If it spins easily and doesn’t feel like something rattles or is broken inside, then you can measure resistance between its terminals and, if there is no obvious short, try to connect it to a 9V battery, and see if it runs.
Then you can measure resistance of the FB1, FB2, and FB3 components on the board. If the theory that FB2 is burnt out is correct, than resistance of FB1 and FB2 should read close to zero, while FB2 reads open circuit.
If the motor is still under warranty, you can always ask VEX support about replacement options, otherwise…
VEX is unlikely to give us any specs on the unmarked parts, so if your school is planning to compete in VRC and you believe in right to repair, then I would save this motor in a special box to be used later for harvesting any usable parts to repair other motors in the future.
If this is for classroom use only, your school is tight on budget, and you are not afraid of soldering, then…
No light of any sort may be an indication that something else got damaged during a short circuit event (i.e. crushed motor brushes).
After disconnecting the DC motor from PCB you can open up another working motor, connect them both to a V5 brain and start measuring and comparing voltages (vs ground wire) at various points on the PCB.
This could lead you to discover if any diode, resistor, or voltage regulator along power route is damaged.
Burnt ferrite bead, diode, resistor, or capacitor would be relatively easy to replace, rather than other more complex active elements in the absence of schematics.