Sometimes for some reason this bit of the story fails
You should go back to an earlier save and try doing things in a different order - not the order given in the walkthrough on the Wiki - for example :-
I started again from a save at my arrival back in Port Royale from Vane's hideout. & talked to Woodes Rogers outside shipyard as before.
Picked up Surgery kit & medicine chest - talked to Grandma - talked to Selkirk in Bootyroom - then Caroline K & got jewelry.
Sold jewelery - bought antidote & Etherbottle
Went to church & talked to Cook outside - he opens half the chest.
***From here if you follow the order in the walkthrough - go to port - keys from boatswain - talk Apothacary - Rogers Shop & buy Violin - get violin & items in Grandmas room - go to port and give Apothacary violin - go to Library & talk to Rogers <<<<----- here you get the dialog screen with no dialog & Dampier is not in Gunroom - Claire Voyant & Dover are not in their places. ( Tried this several times )
SO after Cook opened the chest I went straight to the Library - Rogers talked to me OK -- went to Gunroom & talked to Dampier ( checked that Voyant & Dover were now in place )
THEN I went to Port - got keys from boatswain - talked to Apothacary - went to Rogers Shop & bought Violin - get violin & items in Grandmas room - go to port and give Apothacary violin
Then talked to Dover - talked to Claire Voyant & got her items -- went to tavern & got bottles - went back to Dover and collected his medicine
Talked to Rosabella in Crews Quarters & got her item - went to Booty room & talked to Selkirk and got Friday's leaves - went to Food cellar picked up Food Chest - collected food & took it to Cook at Church -- went back to food cellar & recovered Medcine Chest - talked to Grandma Rogers ( tells you to go see Stretton the Gunner) -- go to Armoury ( powder monky by door) & gunpowder Storage.
Try this and see if it works.
Quote taken from original post here:---->>> http://forum.piratesahoy.net/index.php/topic/11724-jrh-quest/page__view__findpost__p__413155