I have read that eating layer feed is very bad for chicks, but I imagine it depends on whether it is their sole ration (i.e. if the broody is teaching them to forage). As I understand it, if they are living solely on layer feed, the excess calcium destroys their kidneys while the lack of protein slows their growth. Perhaps someone more experienced than I am will have some more insight on this.
How many chicks have died, and how far apart? If they all died within a few hours or a day of being without water, it would seem that this might be the culprit. If the problem started before the water shortage, though, that seems less likely. If excess calcium from eating layer feed damaged their kidneys, losing their water supply could be the final blow, taking them to full-blown kidney failure and death.
When you refill the waterer, is it empty? They need to have access to water 24/7, so if it's empty when you refill it, either they need a bigger waterer or it needs to be refilled more often.
When you watch them outside with the broody, are they huddled up together under her (like they're too cold) or running around?
Did they have bloody stool (coccidiosis)? Pasty butt (constipation)? Were they sneezing (respiratory infection)? Any signs of mites, lice or worms?