I just replaced the blower motor in our Lennox G20RQ4E-75-5 Furnace, Original blower model #45H32301 with 60L2201 per Lennox recommendation. Blower can be switched on by the thermostat but then won't shut of when thermostat switched to of. Further When thermostat is switched to cooling fan/blower comes on but not the condenser. I suspect the same with the heating cycle. Any ideas? I followed the instructions explicitly due to replacing with the leaded 5 speed replacement.

How long did you wait for the blower to turn off? Some systems have time delays in them to improve efficiency (cool heat exchanger down and same idea for cooling coil).

There could also be a delay on the condenser. Certain thermostats will flash "cool" until the unit goes through it's delay cycle. There are also time delay relays in some condensers.

There are also several safety switches along the circuit (float switch in pan, float switch in condensate pump, freeze-stat, pressure switches, etc.). Any one of these will stop the condenser from running (as well as time-delay). Check the pan for water, check the condensate pump to make sure it is not full, see if the condenser has a reset-able pressure switch, etc. When the blower failed I'm sure the unit iced-up and there could be water or the pressures went above/below the threshold to "trip" it the pressure switch.

As far as the condenser goes, it should be getting 24V to the contactor. The relay will be pulled-in, and making the electrical contact. You can check this easily by carefully placing a Volt meter on the two low-voltage wires that go to the sides of the contactor (or you can see that it is pulled-in). The unit gets it's 24V off a low voltage transformer in the air handler. You will see a two-wire cable that runs outside with the lineset. One side of this is connected to "C" on the transformer, and the other side will be connected to "Y" from the thermostat (the thermostat connects Y for the cooling relay and G for the fan relay to R for Cooling, and W to R for Heating).

Hope this helps. Try turning it to "Cool" and "Auto" and waiting for at least 5-10 minutes. If nothing happens then check if the thermostat needs batteries, or if there is 24V on Transformer (usually reads around 26V). You should have power here because the fan does come on. As far as it shutting off, again wait 5-10 minutes.