Broken means non-functioning.
It may imply that some parts of the object are separated from its physical instance, but the main information that the word "broken" gives is about the inadequate state of functionality.
Faulty however, does not by itself make any statement about functionality but rather about the normal or original state of the object and our expectations.
A faulty object isn't necessarily non-functioning, but it just isn't the way it was originally meant to be or isn't alike other objects of the same class in some negative way.
I'll make an example: A car can be considered faulty when, it was intended by the manufacturer to be red, but instead turned out to be pink. If you can still drive it around your neighborhood and don't worry about looking bad, it is faulty but not broken. If, however, a tire is missing, it is faulty and broken.