Whats wrong with my RES turtle?

I was given a turtle and was not prepared for it. I've had it for almost 2 weeks and I haven't seen it eat the Repto Mini baby food for his kind. I change his water every 2 days if I'm busy, and let him bask anywhere from 2-8 hours depending on the day. I don't have a proper dock for it, so it depends on me to let it out under the light. Anyways, all it likes to do is huddle in the corner and "sleep". Sometimes it seems he's dead because he hardly moves. Also, his shell has just started to look dry with white spots down along the center midpoint. I want to donate it to someone who can afford to give him a better life but right now I'm concerned in just keeping him alive while I find a place.