.. How can I open the cabinet?

You need a key.

Or maybe a toy key would work.

Where can you usually find cheap toys?

These include decoder rings, stickers, keys, and other prizes.

There aren't any Cracker Jacks aboard this ship.

But there is cereal.

Have you looked at the cupboard in the kitchen? (You can reach the kitchen by going down the hatch behind the mast on the main deck and then by going through the door at the back of the sub-deck screen.)

Take some cereal.

You need to open it to get at the prize.

And you need to open the prize to get the key.

You can now unlock the cabinet in the captain's quarters.

Open the chest inside the cabinet.