With the belt on the drum, the motor turns with the assistance of a push. Makes a heavy buzzing noise. If you try running it with out a push it make a very loud buzzing noise

You will need to replace the motor. The start winding has burned out, or if you have a start capacitor it could be bad and all you would have to do is replace that. Most dryers don't have start capacitors, however. You may be able to find a used motor at a used appliance shop for $10-20. Those motors usually last a very long time. If you clean it out and put in a new belt after replacing motor you will have a new dryer. Get some white lithium grease and grease all bearings, too. DrTom4444