A basking light isn't designed to heat the entire enclosure, just a localized area. You need a temperature gradient in any tank and if it's too hot under the light he may burn himself while basking. If it's too cold in the basement by all means use a heater for the water. These shouldn't be turned on and off however as they can take a fair amount of time to heat a large body of water. Set the temp on them to low to mid 70's and leave it there.

As far as food, try LIVE earthworms. Turtles are attracted by movement and they seem to find them irrisistable. Also try Mazuri and ReptoMin food sticks, feeder fish, Duckweed, veggies, crickets, mealworms etc.

It may take a while and some effort but he should start eating.

Painteds can go a couple of weeks without eating and provided they are active and show no other sign of illness you shouldn't worry.

If all else fails take it to a vet, just don't leavr it too long.