Talk to the Lost Welshman.
Read the encyclopedia.
MegaMonkey -- use your teeth to remove the cork from the shaving cream bottle.
Use the needle on the magnet.
Put the needle in the cork.
Use the measuring cup on the seawater.
Put the cork/needle in the measuring cup.

Give the compass to the Lost Welshman.
He will take you to Skull Island.

Skull Island

Talk to the winch operator.
Have him lower you down.

Use the umbrella while you a falling....

..and enter Smuggler’s Cave.

Talk to the pirates.
Play poker with them.
When you get your cards, use the 5 cards you got from Madame Zima instead.
You have 5 of a kind;  you win.
Pick up the diamond.

On to the final section of Part IV ....