Is it a thermostat problem (possibly batteries need replacing) or AC problem? The AC won't come on when the fan is set to AUTO. It will come on when set to ON, but it just gets colder and colder and it doesn't matter the temperature I have it set on. The thermostat was installed in 2004 (new AC unit in 2011) and worked fine until now. If it's just batteries, how do you replace them? Thank you.

Looks like that stat has 3 batteries. You'll have to remove the stat to get to the batteries. The stat should snap off of the wall plate.