DIAGNOSIS The thermostat is not detecting the actual equipment state. This is a wiring or configuration issue at the thermostat.
FIX Go to Menu > Installation & Wiring > Equipment. Select 'Reconfigure Equipment'. Run through the setup wizard again. It will test each wire (Y, G, W, etc.) for voltage. This recalibrates its detection circuit.
IF THAT DIDN'T WORK The relay on the furnace control board that corresponds to the stuck signal (Y for cool, W for heat) may be fused shut. You'll need a multimeter to test for 24VAC at the thermostat terminals when the system is 'off'.
HEADS UP A fused relay on the furnace board requires a pro to replace the board or relay. Do not attempt if you're not experienced with line voltage.