The thing that strikes me about your set up is that the thermometer is at what should be the cool end of the brooder and the water is nearer the heat lamp and it is a closed sided box. That means that the heat will build up in there with no place for the chicks to cool off and the water will be warm, which means that cocci will thrive in it. If you consider that this brooder is in a warm room with ovens being used, rather than a garage or spare room where the ambient temp is cooler, then my gut feeling would be that they have either overheated or it has become a breeding ground for coccidia.
I might be reading the situation wrong, but if they were under a broody hen, they would be running around outside in the cold and just ducking underneath the broody to warm up when they needed it..... I've only ever raised chicks with broody hens, so I may be speaking out of turn, but they do not need to be warm all the time and in my opinion it is unhealthy for them to be kept at a constant temperature