I would therefore think you do in fact have an electrical problem.
Switch it off. Get right down near the motor, then listen as you switch it on.
If there is no hum at all, leave it on for a while, then see if the motor housing gets hot.
If there's no hum and it remains cold, then you have a break in the connection, best case,
the wires aren't on properly or are broken and need to be replaced.
Another simple cause is the thermostat is broken, and not requesting the motor to start.
Worst case the winding on your motor are blown and you'll need to replace it. Only, replacing the motor causes you to lose all your gas, so you'll need it regassed too. If you have this don't professionally, they will save a fair amount of gas for you.
If there's no hum, and it gets hot, the diagnosis is similar, in that the motor is likely to be cooked, as there's a short between the windings.
Standard tech assist would have me ask if it's plugged in (light's on so we assume yes)
Next question would be: is the thermostat set to 'cold' it may not be broken, only set wrong.