Humidity could certainly cause issues, though they would be more permanent, and wouldn't be contingent on your AC being on. Have you checked to see if your AC is affecting the current draw on the house? My guess is it's using so much power off the circuit, the set can't power up. Many sets have automatic protection for extreme brownout conditions.
Thanks, but it is not a brownout problem. During the winter months in Florida our house is open (no heat or air) and the tv comes on as expected. When it becomes too hot outside we close up the house and turn on the A/C. That is when it becomes an issue whether the A/C is running or not.