Translation:I am very sad because of being broke.
Đang is a marker for something that is/was/will be in the process of happening. It's equivalent to the English suffix -ing or 'in the state of'. I'll give you 3 examples:
Hôm qua trong khi tôi đang ngủ... = Yesterday while I was sleeping...
Tôi đang ở trường học = I'm (currently) at school
Tôi sẽ ngủ ở trên máy bay trong lúc bạn đang còn làm bài thi = I will be sleeping on the plane while you are still doing your exam
DL rejected "I am sad because I am broke." This sentence doesn't mean anyone else is broke, does it?
I agree with all the others. "Because of being broke" is not good English. There needs to be a subject for this clause.