You need to call a tech to have him come out and look at your unit. Sounds to me like your contactor is welded shut...or you have some crud in between the points... like dead ants,stuff like that.

Hope this helps

Try this. Turn off the breaker for the outside unit. Activate the thermostat in the house and have someone outside listen to see if they can hear the relay clicking in and out. (noticeable clacking noise). If nothing is heard then probably a bad thermostat.
Also, it would be cheaper to go to Home Depot and get their cheapest thermostat for a test than to call out a technician. If that cures the problem then get the thermostat you want.