It is likely he has done the motor, yes.
It is also likely he has done the PCB and/or the cleaner head motor.
Depends how long he ran it really. Its hard to say without testing each component.
You could get a 240v motor and full cleanerhead, which would upgrade the machine to Euro voltage. I am not aware any other components differ.
You cant get 110v stuff in Europe that I know of, if you want to stay at 110v, you would have to order in the US and ship it (but you have military mail so that wont cost a lot).
Really, what *some* would do in this situation, if they wasn't inclined to take it to bits, is ship it back to a friend/family member the US with that nice military mail service, get Dyson to repair it under warranty because it had 'just stopped working' and ship it back again.
Question: When plugged in the 110v, even though the main motor doesn't run, recline it and see if the brush roll fires up?