A few days ago everything worked fine. I left for a few hours and when I came home that night only the fan worked and it wouldn't shut off. The thermostat looked to have gone mad, the temperature reading on the thermostat was changing up and down within three degrees despite that fact that the air temp. Coming out of the vents wasn't changing. I swapped out the thermostat, because I hated the old one, and was hoping that would solve my problem. Predictably it did not.

A couple of questions:

1.When you say fan stays on do you mean the indoor blower motor with air coming out at the registers?

2.Is the unit a split system or package unit (http://www.thermal-medics.com/a-c-image-glossary/)?

3. If a split system does the outdoor unit (condenser fan and compressor (http://www.thermal-medics.com/a-c-image-glossary/)) come on?

4.Can you turn off the thermostat completely and have the fan stop blowing?

Sorry, double post

1. Yes, it's the indoor blower.

2. It is a split system.

3. The outdoor unit doesn't turn on at all.

4. I haven't tried it with the thermostat unwired, but with it set to off the fan continues to blow.

One troubleshooting tip is to take a small wire nut and connect the red and green wires on the thermostat (after removing the t-stat plate first).

Just keep all the wires nice and separated at first then go red to green.
1. Does the indoor fan come on and then turn off when the wires are separated?

If yes:

Now take red, yellow and green and connect with wire nut.

2.Does outdoor unit run with indoor blower motor. (you may get heat or a/c in this config - does not matter)

If all this works look at a new thermostat. Please update on your progress and success. Thanks