How do I turn off the power to my programable thermostat?
See if you can open the old unit and check for batteries.  Many of them have them in case of a power failure.  If you also have another air conditioning unit, you will want to throw the breaker or pull the fuse for it as well.  My system at my old house had two fuse boxes mounted outside the unit as well as another breaker in the box where the main power came in.  I definitely had a unique setup, but I'm sure there are others just as unique.

I hope that helps!