You need a crew member who's big...
And has a talking tattoo.
Talk to Meathook. He lives in the house at the yellow light (labeled "Shore" or "Island") on the general map of Melee.
How do I cross the ravine?
Like every other crew member you'll get, he doesn't know that the Governor was kidnapped by LeChuck.
Like every other crew member you'll get, tell him about Elaine's abduction.
Maybe he'll be on your crew.
Why don't you offer him a position?
He'll want you to prove yourself first.
He wants you to touch the murderous beast that gave him hooks for hands.
So open the door, and touch it. The rest is automatic.