I don't want to be the bearer of bad news...but, the first mistake you made was in putting them in a corner of your big chicken coop, cage or not. Domestic poultry carry diseases that won't display on your chickens but are fatal to your quail. If without the direct contact, birds are dusty, dander throwing fools. On your own biosecurity, you pass through the chickens first, and by handling those birds first, you could be the vector.
Unfortunately, there probably is little hope for your remaining quail, but you can start again. Put the cage or pen for quail, well outside of where your keep chickens. Don't use the same the tools (buckets, waters, feeders, even cleaning equipment) for both. Take care of your quail first, then chickens...change shoes.
I feel bad for your losses and wish whoever sold you either birds or eggs to get your start had told you Quail 101 before you got them.
Don't be discouraged, try again!
Good luck
