The first signs of a dryer motor going sour can be a loud growling or buzzing when you push the start button, or a motor that shuts off before the cycle is supposed to be finished. Cleaning dryer vents and making sure the motor is not covered with lint will help prolong motor life; motors that are covered with lint are likely to overheat and burn out.
If the dryer hums but does not tumble after you press the start button and cannot be turned by hand, your motor may be burned out and need to be replaced.
If you are unable to rotate the dryer manually, and the blower fan housing is clear, you will likely need to replace the motor.
If the motor rotates freely, attempt to run the motor with the belt removed and the blower in place. If the motor runs fine with the belt removed, the idler pulley or clothes drum may have problems. If the drum will not rotate fully once the belt is on, you may need to replace one or both of these parts.
If you have to hold the start button for more than a second, this is probably a sign of a burned-out or bad motor and will probably warrant a replacement.
Thermal Overload Detector
If your dryer stops after only a few moments of working, your problem might be in a malfunctioning thermal overload detector -- these devices are mounted on the motor and on the heater box. Troubleshooting the motor can allow you to distinguish whether the TOD or motor is actually the issue.
If the motor hums but does not rotate on its own even with the belt removed, but can still be turned freely by hand, you may need to replace the motor or the motor start capacitor.