Have you measured the temperatures in the water and on the basking dock with a thermometer? That's the only way to tell what they really are. GThiele93's advice about temperature is good but you won't know if you've got the temps right unless you measure it with a thermometer. We really cannot tell just by how it feels what temperatures are since we are warm blooded.
Here are some tips on enticing a turtle to eat:
http://www.redearslider.com/entice_eating.html
Keep in mind that while cool temperatures can cause a turtle to slow down and lose his/her appetite, another thing that can cause this is illness. If a turtle's water is always too cold, if they aren't feed a good diet, if their water isn't kept very clean, and if they don't get to bask under good light, then they will get ill. When a turtle gets a serious illness like a respiratory infection, the only way to save him/her is to see a vet and get antibiotics.
On the diet, it sounds like your turtle needs a much better diet. A turtle's diet is very simple - pellets and green vegetables supplemented with occasional treats like carrot, bell pepper, blueberries, sweet potatoes and tomatoes - but its important that they have the veggies and that they have variety in their diets. Also, it's very important that they have a good calcium source like a cuttlebone in the tank. You can get a cuttlebone for a dollar or two at the pet store in the bird section. Here's some good info on diet you should read up on:
http://www.redearslider.com/index_nutrition.html
The other big concern is basking and light. Turtles have to be able to dry off completely - top and bottom - at frequent intervals or their shells will become infected. They do this by basking. The other thing they get from basking is UVB. UVB light causes a turtle's body to produce vitamin D. They have to have vitamin D in order to absorb the calcium they eat. Without the calcium, their shell and bones will get soft and eventually they will die. Only light bulbs that advertise that they provide UVB will actually do this. There's a brand of UVB bulb by Exo Terra called a Repti Glo 5.0 26 watt bulb that's not as expensive as some of the others but is probably a good choice.
I think GTHiele also made an excellent suggestion about working to get money to take care of your turtle. If you get an allowance, can you save from it to get the equipment and setup your turtle needs? Your turtle is relying on you, so see what you can work out.