.. How can I get past the rat?

Look around the room.

The rat has a bowl.

Bowls are usually used for eating and drinking.

This rat is thirsty.

Do you have anything it might drink.

Something alcoholic?

Like grog?

Grog usually comes in bottles.

Have you seen any bottles?

One of LeChuck's crew members has a bottle of grog.

Although he isn't exactly awake.

Have you visited the ship's sleeping quarters? It's down the hatch on the main deck.

The sleeping ghost crew holds a bottle of grog.

How can I get the bottle from the sleeping ghost?