I just want to clarify that you had an initial thread on this issue and that you don't know it was respiratory problems, you only know that before it died, it was opening and closing it's mouth to breath.
If you post that your chicks are dying from respiratory problems you are going to get different advice, all having to do with it being contagious and with giving antibiotics and people will ASSUME you know for sure it's respiratory problems.
I know you're new, so welcome to BYC, but wanted to help you get the best advice possible. First, it's best not to start another thread about the same issue because some of the facts get lost and it gets too hard to follow.
Second, I'm not sure it was a respiratory problem. The chick was only one week old and didn't have runny eyes or stuff coming out of mouth or nose - from what you've posted. You didn't say how long before it died that the mouth breathing had been taking place. I posted on the other thread it could have been panting because you said the other two chicks were also now acting lethargic.
To get the best help - please list all symptoms and signs that you know and others will chime in and try and help.