で can be used to represent causal relationships in a similar way to some english uses of
because, although I am hesitant to say that
because. Your two uses of
に do not really work; I would stay away from trying to use
に as "because" in most cases.
Let's talk about
で though. You've actually picked two very good examples, because although the
で in each of them is representing a causal relationship, they do so in different ways.
で is an abbreviated
であり. You can read more about this here, but this is very close to an English
and, and it can be used to represent causal relationships in a similar way.
The lobby was full (of people) and I could not get in.
because necessary. Also note that
This is the
で particle we know and love.
悩み事 is the thing directly facilitating somebody not sleeping, in the way that the plane in
飛行機で行く directly facilitates your traveling.
I think it's safe to translate this as "I could not sleep because of my worries", but I encourage you to think of this more as a natural extension of the way
で is used than as it corresponding directly to
Edit: It might be best to think of
because of, rather than just
because, as the possible translation for
で here. It really only plays this role with nouns, which in English will end up as
because of [noun].