Oh Geez, Bummer!...but not surprising. I'm so sorry you're having such rotten first time luck, hard way to start out.
I conclude that those chicks had something wrong with them from the get go, disease or internal deformity.
Any way to quietly review that hatchery's reputation? I would not buy from them again, that's for sure.
Sad the last chick will likely succumb, but makes moving forward simpler in a way.
Sanitize the cage and all equipment with a strong bleach solution, let all air dry in the sun for a week, and start over with chicks from another source.
What a heart breaking experiencing for you. I agree with aart. Clean up and then get your babies from a different place and start over. It doesn't sound like you did anything wrong. Sure, one or two can die, but when it is that many, there is a problem. In addition to other things, it would bother me that he isn't on site to catch a potential problem as it starts.