Your Cub Cadet 1024 Hydrostatic lawn tractor is designed to cut and maintain large lawns. It uses hydraulic fluid for steering and gear shifts. But it can't do anything if you turn your engine on but the tractor does not move. Troubleshooting this problem includes examining key systems that stop or move your 1024.
Operating the Cub Cadet 1024's brakes normally entails pushing the brake pedal down and holding it while gently pushing the parking brake lever down. Releasing the brake requires depressing the brake pedal slightly. If there is a problem with the brake rod and its connection to the brake discs, the brake won't release and will keep your tractor in place. Have someone examine the rod's action to see if it's fused or broken while you repeatedly operate the brake system. Also check to see if the brake discs are seized and not releasing.
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If your Cub Cadet 1024 was moved manually, the problem could be with the hydrostatic transmission. The hydrostatic relief valve must be opened and the bypass rod must be pulled out before a manual move. This allows the transmission fluid to bypass its normal route so the tires can freely rotate. If these were not returned to their original position, the transmission will not operate after engine start.
When you shift gears, the transmission v belts operate the hydraulic pumps to move your Cub Cadet 1024's axles accordingly. While small cracks are normal on V belts, any wear or tear indicates that they need to be replaced since they can't be adjusted. Only replace them with factory-issued parts to ensure a good fit. Off-brand belts may not disengage properly and do further damage to your mower.
Your engine has a belt that engages the mowing deck and works with the idle pulleys as well. This belt is also subject to wear, tear and slipping off of pulleys. If this happens, your mower's engine will remain on but it won't move. Keep grease and other lubricants off of the engine belt. Also check the pulleys for damage that may cause slipping or tears on the belt.