Bryant model #563cn030-b when i turn on thermastat inside th house i go outside and only hear a low hum, then i

SOURCE: fan not blowing

Even when the power is off at the unit outside the thermostat will supply power to the contactor of the outside unit. This may give a hum or buzz as you stated. If when the power is on to the outside unit the fan tries to start but only hums the motor may be bad. Does the compressor start and run?

SOURCE: AC fan not blowing/ Honeywell T87F thermastat

if you have a voltmeter that checks capacitance, check the capacitor ( silver looking battery) that is mounted on the side of the blower housing in the furnace. You need to take the wires off!! A bad Cap will slow down the fan and if its blown/dead the fan will not run.

If youre more than 1 MFD off the rating stamped on the capacitor, Replace it.