a/c blower fan turns on in "on" position. As soon as t stat is set to "cool"(blower in "on"or"auto position) the fan turns off and outside condenser unit does not turn on . The heat works normal. Main electrical power from breaker panel is fine. The outside condenser unit will run if the relay on the unit is manually ingaged. Any help or advice would be greatly appreciated...

It sounds like your circuit board needs to be replaced. Turn off the power to furnace. Remove the circuit board from furnace without disconnecting any wires. They sometimes show burn marks on the back of the circuit board when they go bad. (Not always) the circuit board is on the lower half of the furnace. Some are enclosed in plastic of either a beige or black plastic. You'll see a lot of wires going to it.
Hope this helps.

If you changed out your thermostat be sure to ad the jumper wire from RH to RC on the thermostat sub-base.

Make sure that the thermostat is wired correctly as T-Top mentioned RH and RC need a jumper. The yellow wire needs to be connected to the Y terminal and at the furnace their should be two wires coming from outdoor unit. These don't matter what color they are. Typically they are red and white. One should go to Y terminal at furnace and the other to common or C terminal.