Well, it translates more into "No", and impossible is a little too strong for this i think
Are there any notable differences (such as in context) between "不行" and "没门" ?
For example, when a child asks his mother "我可以出去玩吗？May I go out to play?" Then the mom may reply "不行！" if the child hasn't finish his homework.
This is a simple way to refuse some one, direct (or maybe impolite) but not rude.
I believe 'cannot' is acceptable as an answer. For example someone asked to borrow something. An answer like 'cannot' should be acceptable