The house is not cooling

Lots of possible causes, but you may need an HVAC repair man to diagnose it. The first thing they'll check is the refrigerant levels (Freon, Puron, or whatever your system is using). If it's low, there may be a leak, possibly caused during the blower motor replacement.

Simple things you can verify yourself are that the outside unit is unobstructed to allow air to pass in the sides and out the top. If it isn't even turning on, either your refrigerant levels are so low the compressor is staying off for safety, or perhaps it's as simple as a wire not being plugged back in from the thermostat to the inside unit. The owners manual should include a wiring diagram.

Another simple thing to check are any filters either on the return vents or at the blower itself. And finally, open up any access panel you can on the condenser coils and make sure they are clean and free of ice.

I ended up calling a buddy of mine who is an HVAC tech and he pointed me in the right direction to check the fan wire on the back of the thermostat. I checked the wire and it was just hanging in the terminal. I'm pretty sure that was the cause of the problem. It makes sense because there wasn't anything wrong with the blower motor itself.

The fan wire on the thermostat was in fact the problem. I fixed the connection and it has worked fine for the last 3 years.