1 month old kitten, lethargic, not eating, help!?

So our cat just gave birth to four kittens. In the beginning, there was one kitten--let's call it B--that was smaller than all the rest. Not by very much, but as the kittens started to grow, this one seemed to kind of lag behind physically. However, it was the one with the most personality. It started to play before any of the others, it was always rolling on its back, and it looked like it was feeding nicely. Then one day the mother cat got sick. She was vomiting, but she got better. It seemed like one of the other kittens had come down with the same thing but bounced back quickly enough. However, B seemed to take a horrible fall in health as the mother did. It started sleeping all the time. It wouldn't nurse--in fact, it would crawl away from the mother. I started noticing that it seemed almost ravenous, but every time we tried to put the kitten with her mother, it would just fall away from the other kittens and mother, which it didn't do before. So my mom and I started to take turns nursing it. It's been a couple of days and B has gone down hill very, very fast. It's never hungry, it's incredibly lethargic to the point it barely moves and just sleeps, and pretty much falls asleep in our arms as we try to feed it. The mother and kittens have abandoned it and sometimes it whimpers horribly. Don't advise going to a vet, we're on it, but if you have an idea as to what is causing this and ways we can possibly go about to helping it get better, that would be great. Thanks!