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I haven't posted in here since I first rescued this baby turtle from a friend who wasn't qualified to take care of it. Now I'm hardly more qualified, but at least I have a sunlamp, no sadistic cats, and actual turtle food. Anyway, I've been worried about my Hippo for a while now, cause I really just want him to grow big enough so I can give him to a local pet store and they can sell him to a family who actually wants him. I'm told that its actually illegal to sell a turtle this little (about the size of three fingers held together), so I've been taking care of him until he's big enough to get rid of.

I think I should explain his current surrounding first. I had a heater and water cleaner a while ago, but the heater exploded and I stopped using any of them out of paranoia, so I've instead been keeping him in a plastic drawer filled with water, inside the tank. The drawer is about twelve inches by seven inches, and is about three inches deep with only two inches of water.

Recently though, he hasn't been eating much. I'm thinking it has to do with the weather because we've been going through waves of heat and cold in the unpredictable northeast weather. He's not having any trouble swimming since if something startles him he'll dive in and start desperately swimming into the corner of the tank. But he's gotten more relaxed around me. Anyway, there is one other problem, which I think may have something to do with my bad luck with pets. I treat my pets well, but I tend to have a lot of escape artists. And Hippo always winds up pushing himself out of the mini pond, and onto the main part of the tank, then spends the day tapping at the glass in an attempt to escape.

I'm probably not the best person to take care of this guy, but I don't know anyone who has any experience with turtles, and the pet store can't take him until he's bigger. With all the escape attempts and avoiding eating, I think he's unhappy but I can't really do much more for him.

First, what is the purpose of the drawer? Just give Hippo full run of the tank. Does he have a basking perch to rest on? If not, he'll need one. You can buy or make one.
Secondly, you'll be fine without a heater for now as it's so hot I don't think you'll have trouble with the water going below 78 unless you have A/C... in that case, you'll need a new heater. If you don't fully submerge the submersible heaters or put them in water that is much too cool, they'll explode so you do need to treat them with a level of care, but on the whole they are safe and easy to deal with.
It sounds like Hippo isn't eating because his habitat is too stressful to him. One you get his tank settled, he'll begin eating.
Also, I am confused did you say you stopped using the filter too? You should definitely start using filtration. Dirty water doesn't entice turtles to eat and it can make them ill.
Finally, do not give him to a pet store, they do not find responsible homes. Try to contact a local herp rescue or place an add somewhere where you can ask the potential owners questions to make sure they'll give Hippo a good life.

Everything megcornell said is good advice. Look on this list of turtle recue organizations and see if there's someone near you that will be able to help out.

www.turtlehomes.org

Pet stores for the most part are very poorly equiped to take care of an aquatic turtle and his prospects would be extremely poor if turned over to one. Since you've got him, it's up to you to make sure he stays healthy until he gets a home that's better prepared to care for him. Since, as you are aware, you're not prepared to offer him a complete habitat, you should try to get him relocated as soon as possible before he gets sick.

Basically I have an empty tank, but inside the tank is the plastic drawer which is filled with water and several large stones piled so that he can hide under it, or climb up and bask on top of the largest one. I stopped using the filter because there's no room in the drawer, so I just clean it once or twice a week. Its somewhat stupid of me since red ear sliders are aquatic, but I don't use the tank itself because my mum keeps insisting that he could drown.

Just for clarification, the drawer isn't like a bedstand or anything. Its just a clear rectangular tray that was removed from an office drawer set my parents threw out.

He won't drown, don't worry about that. Just let him have the whole tank for swimming and other turtley activities. He'll be much happier.

He definitely won't drown. RES's are born with webbed hands/feet and are natural swimmers. They aren't like humans who have to "learn" to do anything. RES's JUST DO IT, with no issues.

I agree with what other people said here already: fill that tank up with water. Your RES will love you for it!

FYI - my big Sheba girl is in a 90 gallon tank. I fill that up so much that her feet don't even touch the bottom, not even when she is fully stretched out (my turtle's shell is 9 inches long, and when she is fully stretched out, her full body/arms/legs can measure almost 14 inches long....I keep tank at about 18 inches of water)! She just floats happily, and if she wants to get out of the water, she has a basking dock.

They need to be able to stretch out in the water if they want.