I'm concerned about the sleeping. Little turtles are usually quite energetic. If they want to sleep all the time, it usually means either that they are too cold or that they are ill.
You said on the previous page that the water temp is between 78 and 83 degrees. Did you measure it with a thermometer? In the absense of a heater, the water temp will adjust to whatever the air temp is. Is the room he's in cool? Until you've got a heater, can you keep the room temp warmer than normal - at around 78 degrees.
In addition to lethargy (ie, wanting to sleep all the time, lacking in energy) another symptom of illness is swollen eyes. Swollen eyes in and of itself doesn't mean illness - lots of things can cause swollen eyes (like certain light bulbs, as was discussed above). Here's a photo of a turtle with swollen eyes:
Other symptoms of illness (specifically respiratory illness, which is common in little turtles) are poor appetite, swimming lopsided or difficulty submerging, breathing with the mouth open or frequent yawning, mucus around the mouth or nose.
If your little turtle is ill, then he needs to see a vet right away. Their chances of survival are much better when they are treated early on. For a respiratory illness, the treatment is antibiotics, so it's not something you can do on your own without a vet.
I hope your little guy isn't ill and that the problem has been that the water was too cold. Keep us posted.