Okay, I feel a little better now. Here is what I wrote, the more I read it, the more I feel he will do the right thing. He is an extremely smart guy, so I hope he doesn't take it the wrong way. But here is what I wrote.
I dont like to sugar coat things, because I believe that effect will make this seem less urgent. But here it is without bashing him in the head. :/

Hello!
Just observed a few things regarding the health of your turtle over these past few weeks; he is sick.

He has runny green stool. Correct me if I'm wrong, but it's supposed to be whole and soft/squishy. I believe it can be corrected with an assortment of green veggies/fiber once daily like: romaine lettuce, collard greens, vegetables, squash, sweet potatoes and some non-citrus fruit DAILY. Also, earthworms and meal worms will restore his depleted fat deposits. You must change his water whenever he soils it or at least daily. With him sick it will create a bad circle of events.

If it continues, he may develop kidney and liver failure, and his blood will become toxic and he will die. If it continues like this and doesn’t clear up, I do know of a very good reptile vet in Auburn that will probably be able to help you. Your turtle is still young enough that it shouldn't have any lasting harmful effects if we catch it early.

His beak is getting too long and the overbite may start to inhibit his eating habits, which could be the reason he is skinny. I suggest a cuttle bone and flat rock as a food dish. The cuttle bone will provide calcium as well as keeping his beak in good condition.

His back toenails were seriously warped, damaged and much much too long. I have trimmed them to a reasonable length. To keep them trim without the manual clippings, provide a larger rock for him to scamper around on (I know this will almost require a larger keep, but we will get on to that)

His shell is dull, dry, crackled and slightly deformed. It should be shiny and hard. This is from lack of a well rounded diet and poor vitamin nutrition. Your basking lights are only good for 4-6 months, as the vapor creates a film on the inside of the bulb, preventing UV rays from penetrating. He is in serious need of some good 'ol time in the sun. Taking him outside for a half an hour a day will do TONS of good to get him better in conjunction with the bulb. He needs it to be on a 12-12 hour’s schedule. Not doing so will stress him out further, and keep his immune system in the rut. You may even have to give him a calcium supplement twice a week to help him recover; otherwise you are putting him in risk of shell rot.

Speaking of shell rot, I have thrown out your old reptile carpet, and bought you some new ones (it was bad man). The old one was growing black mold in his hide and underneath the food dish. I have sterilized the food dish, and cleaned up most of the mold. His carpet needs to be washed in a weak bleach solution once every week, rinsed and hung to dry. There is an extra carpet for switching them out to do this. You may even need to switch his water dish to a ceramic (dog dish) one to help with his nails.

MAJOR CHANGES NEEDED
Depending on his species, they need a high level of humidity to prevent RI's (respiratory infections) and keep him healthy. You currently don’t have any thermometer/hygrometer to measure this. Nor do you mist him. I have read that American box turtles need 70-85% ambient humidity. "...kept warm (85° F ambient) and humid, fed regularly, and not allowed to hibernate." I'm going to say he is currently at 45-50% humidity, most likely 30-35% because of the 2 overhead heat sources. This is crucial in bringing him back to health. I can show you a great DIY to create a high ambient humidity with a screen cover. In the meantime, I suggest a brick of coconut bark as substrate or cypress mulch to keep it moist.

On top of all this, all the literature I've read suggests a much bigger enclosure for your turtle. I would even suggest dumping the tank all together and buying a rubbermaid/sterilite tub. They are extremely successful habitats, and while not appealing to the eye, it will be very beneficial for your turtle. If you want more current care sheets, I can print out ones species specific for you.

Please read through this with an open mind. If you want some more advice or setup help, I am more than happy to assist you along the way. If you decide you don't want the turtle anymore, we can talk about your options. Thanks a bunch!