I have a day and night carrier unit. I took the cover off the furnace side where the ignitor is there is a small blower motor with a squirrel cage on one side and a small bladed fan on the other end, it turns freely until I turn on the heater than it just hums and locks the little blower motor up, the larger fan that blows the air through the house is running but seems to be very slow.

First thing I would do is with a meter check the voltage coming in to the furnace,it should be very close to 120 volts, and if you can check voltage going to each motor while trying to run

Sounds like a good place to start, just seemed odd that the motor that was humming bad was locked up only when the power was on, otherwise it spins very freely. Thanks