You could have a bad contactor, shorted capacitor or a defective compressor. All of which are beyond the scope of the average DIYer. Call a quallified service company.
The humming sound is most likely the compressor running. Since the fan is not being turned on while the compressor is working there is possibility that there is a problem with the fan motor. The first thing you should do is turn off your air conditioner. You don't want the motor to burn out. Then call a repair man.
The contactor can be bad, the condensing fan can be bad, or the compressor can be bad. It's also possible that it's not getting a control signal from the thermostat.
AC Units greatly differ by brand. Since there are some many types of brands I would insist that you refer to your particular AC User Manual. They are quite useful.
The humming noise could be the thermostat sending a signal to the contactor, telling it to come on. Check your power to the condenser unit, may be at the meter panel. Breaker could be tripped
