Welcome to the forum!
I'm sorry about your baby turtle. You brought the baby in recently? It's best to either bring them in in the fall or keep them in the pond. Fast temperature changes can mess with their internal clocks and so on. Even if he's warm now, he thinks it's winter (albeit a warm one) and that he shouldn't be eating. What kind of lighting and heating are you using? How big is the tank? What is the water temperature? If the water is 75 to 80 degrees F, he would start to eat soon if healthy. If less than that, it will take longer, and he'll eat less.
A healthy turtle will not "swim" upside down. I'm afraid that that is a very bad sign. Can you take him to a reptile vet? You assumed he was dead, and not responding would have indicated that was true. It's amazing that he withstood being left out in the open and dry outside in the winter. The bubbles out of the nose are a common sign of an upper respiratory infection but could simply be related to dying and/or being left stranded. If it is an infection, it is often curable with injected antibiotics which you can only get from a vet. While the odds are against him, you should still take him to a reptile vet if you can find one. If that is not an option, then put him in water at about 75 degrees F. This should be at least a few gallons of water. If less than 10 gallons of water, change all of it every day. It's vital that any bacteria and other pathogens are discarded often. Don't worry so much about his not eating as they have stores of energy in their bodies for a while. It's more important to make him warm, alert, and active again. Then, he would want to eat. The best food I suggest is live blackworms from an aquarium store. Other choices are small live mealworms, crickets, and wingless fruit flies. Baby turtles want foods the most that are small, moving, and live. I sure hope you can get him to the doctor, and he can be saved.http://www.fishpondinfo.com/turtles/hatchling.htm
has baby turtle care info.