You do not specify a brand, but whatever serves as a pawl for the drive mechanism has seized and will not release to allow rearward movement.
I've never owned a self-propelled mower, but I would think there would be a lever to engage the wheels for self-propulsion. If the lever is in neutral. I would think you would be able to pull the mower backwards on all four wheels. If there is no lever and the mower is self-propelled at all times, you would have to raise the wheels that are propelled in order to pull the mower backwards.
You are Supposed to be able to do that easily. Oil the wheels. What is keeping it from moving backwards? Look fer it!
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Self propelled mowers are not self driven. The mower has a safety switch which does not allow the unit to turn on itself. A person is required to turn on and steer the mower.
If you bag your grass clippings a rear wheel drive self propelled mower is better . As the bag fills up it adds weight to the rear , which tends to " tip " weight off the front wheels
There were 4 wheels on the first self propelled vehicle, built by Henry Ford.
Had same issue with one of the wheels not turning - removed the rear wheel and found that the pawl was stuck, There is a small spring that pushes the pawl out in forward motion and re tracks when the mower is pulled backwards. The pawl can become stuck in allowing the axle to turn but not the wheel.
There is usually a clutch which disconnects the motor from the wheels. That will make it ok
Broken Belt
6 HP
blade might be out of balance