Thermostat won't work if I press up and down button, battery newly installed.

What thermostat? Some clearly don't work by simply pushing those buttons.

It's my home airconditioning thermostat

Soooooooooo, you are aware most programible thermostats take more that a single button push to change anything.

Again... WHAT thermostat do you have. Most require different steps to change something. There IS more than one brand thus there is more than one answer possible.

It's a "Robertshaw" brand. Actually, when I turn it on for the airconditioning or for the heat, it won't. I was thinking probably the thermostat is the problem but I wanted to be sure before I change it.