On the back of your machine is a little handle. Should be silver and down near the very bottom of the black backplate. It's a transport lock. It locks your transmission up so that if you are moving it on a trailer it won't roll. Try pulling that handle outward and see if the tranny frees up.
Most auto Lawn/garden tractors have a disconnect rod on the rear of the frame. Between the rear wheels you will see a rod/lever sticking out from the frame. Pulling it rearward will disengage the trans. With the brake off it should push easy. The brake will normally work regardless of position. With it engaged you have to overcome the pressure inside the trans. That's why it won't move with the engine off.