The spring on the right deck pulley may be missing or old and stretched. With the engine turned off and the mower deck lowered, reach under the mower frame , grasp the pulley, and pull it forward. Restart the engine. If the mower blades do not turn, the spring is the problem.
I had the same problem and it got progressively worse by shutting off sooner and sooner over one summer. I had the carburetor serviced, but still had the problem. The final solution was to replace the fuel shut off valve in the bottom of the carburetor. This part appeared to be ok, but engine heat buildup would make it fail--an inexpensive repair to a vexing problem! My sincere thanks to a local "back-yard" mechanic who gave me this tip.
The drive belt drives the rear axle and tires. It runs from the front pulley to a pulley located over the rear axle. You do not have to remove the deck. Put the belt on the front pulley and run it above the mower deck, through the belt tensioners, and back to the rear axle. To access the rear pulley, remove the battery and the battery holder so that you can see the pulley from above. Put the gear shift in neutral, or chock the front tires and jack up the rear axle so that the rear tires are off the ground. This will allow the rear pulley to turn freely. Reach through the battery compartment to the pulley, get the new belt started onto the right front of the pulley (you may need to use a flat screwdriver to help ease the belt into the groove of the pulley), hold the belt tight to the pulley with your right hand, use both your right and left hands to rotate the pulley in a clockwise direction. The belt will come around and finally end up in the pulley groove.