Keep getting punted around on the ship...
 

...how do I get into the cannon? (At least I assume that's what I have to do.)

I released the barrels, asked Elaine to light the cannon, and glide the rope to just above the cannon. Now what?

See-Saw?

OK, I found it out after all. Sneaky little door icon finally gave it away... :)

I can't release the barrels because I can't get the key :( There's nothing clickable on that screen (or I can't find it if there is).

Keelhaul time!
If you want to get the timing right, ask someone a favor beforehand.

Maybe it's a "skeleton" key you're after.
Perhaps if someone were to distract LeChuck while you're near said skeleton...

Got the key, but can't find these barrels people are talking about.. And the sword under the ship, do i need that?

Edit: Found the barrels :)
Edit: But what to do now??

See Saw?

You need to contruct a see-saw using the broken door and the barrel next to it.