To answer the actual question, no, I don’t think those things make anyone broken. Broken is a state of mind, and what breaks people varies from person to person. Far be it from me to call anyone broken because of what I see about them. As stated above, if I had to apply that label arbitrarily based simply on my observations, a lot of people would wind up on my “broken” list.
A person is not something like a toaster which has two ways of being – broken or not broken. A person is more than a binary system (yes, I’m aware of the logical problems with that and I don’t care – take it up via PM if you really must) that works or doesn’t work. What I’m saying, ultimately, is that a human being is capable of assimilating experiences and choosing what to do about those experiences. I could choose to be gutted that certain members of my family disapprove so much of my lifestyle that they have cut off contact with me and discouraged people around them from making contact with me. I could also choose to think about it for a while and conclude that my satisfaction with my own life does not begin and end with what those family members think.
How “broken” someone is by their circumstances depends on how they deal with it internally and what kind of help they have externally. It’s never 100% one thing or the other but rather a combination of the two. And, as @wundayatta said, we’re all broken to some degree – it’s a consequence of having a life.