I hate to play Captain Obvious, but...here goes...
Has the OP verified that the license plates are still on her car?
If somebody stole those plates and put them on another car, that could certainly explain the situation.
The ticket must show the make, model, and color of the car that was ticketed.
Does the description on the ticket match her non-functioning car?
If it doesn't match, that is the easiest "out" for her.
If the description does match, she may have a difficult time explaining the...coincidence.