If the gear pack was jammed, the hydraulic cylinder would shred the teeth off it immediately. I know that from experience.
I would try isolating the problem between mechanical and hydraulic. Try disconnecting the cylinder rod from the slide out room. Take a large crescent wrench and try turning the square bar that runs between your gear packs. If you cannot move the gear packs you have a mechanical restriction. If the room moves in or out with the wrench, look for hydraulic problems. To further diagnose these problems, look online for "Hydraulic Lippert Slideout Manual".
Dave