Sometimes you will have to try the next step a few times until the drawbridge is down.
From the alligator screen go to the left.
If the drawbridge is down, there should also be a guard with a cart waiting for something. If not, go off screen and come back.
He's waiting just long enough for you to DO something.
Walk up to the cart and jump in.
Once inside, jump out. Voila! You are now inside.