Hi AJ,
I'm thinking it may be worthwhile to check the motor start capacitor, but would need to know the model number of your dryer to be able to look up information about it. Electric motors take a lot more current to start up from a stop than they do to keep turning once they're in motion. So rather than build the motor with massively outsized power requirements, manufacturers use a capacitor to store up an electric charge that gives the motor a boost when it's starting. If that capacitor fails then the motor can run normally once it gets up to speed, but just can't get going from a stop.
Try holding the door switch closed so you can start the dryer with the door open and manually start the drum turning when you hear it humming. If it runs with a boost to get started, then it's a strong indication you may need to replace the capacitor.