Thank you everyone. This is really tough and your kindness and support mean a lot.
The vet thinks he has pneumonia, which surprises me since I didn't hear any congestion in his lungs. She injected him with fluids and he perked up immediately. I can't believe how severely dehydrated he was. She also gave us Baytrill and Vibramycin.
The prognosis is grim. The vet emphasized how small of a chance he has to make it through this. But we're going to try everything we can until the last second; Jack is a strong little guy and I won't give up hope.
Jack and Bean are the first rats I've ever owned. I think of myself as a responsible and loving pet owner, but in this case I made some mistakes that, had I known better, could have made the difference. I want to share my mistakes here with the forum so hopefully other new rat owners won't do the same things I did.
I did everything right -- giving him yogurt, keeping him warm, force-feeding him water and food. The problem is I didn't do it soon enough. I had read that rats go downhill fast but I didn't realize how fast. Within 36 hours he went from a little skinny and tired to horribly dehydrated and malnourished. And there were no other symptoms -- no sneezing, no coughing, no strange behavior. Just a loss of interest in food and sleeping more than usual. At the first sign of ANYTHING strange I should have taken him to the vet immediately. That was my first mistake.
My second mistake was that I didn't have a vet lined up. When I got the rats in May, I did my research online and found a vet nearby that specializes in rodents and got very high reviews. I thought that was enough. But now, when I need him, I find out his practice no longer exists -- I have to find another vet. Not only that, but I have to find a vet that is experienced with rats and can see me a weekend, immediately. Luckily I was able to find one, but that's only after NINE other vets turned me away. I should have actually spoken with a vet before I got the rats, and I should have had a back-up vet too.
Jack is resting here with me. He has fluids and antibiotics in him now. I know the odds are not in his favor, but I really hope he makes it through this.