Travel to Watchit Island and pick-up the hidden eleventh puzzle fragment (right from pathway to the tower, next to the red cable). Continue in the direction of the radio tower.
Take the damaged transmitter and make an attempt to climb the tower. Oops... you'll need a lightning rod or a person that will work as one - e.g. Goal. You can find the final, twelfth puzzle fragment in the left side of the area, next to a radio tower sign. Return to the trawler and give the transmitter to Doc - you'll receive the fixed device after a moment.
Travel to Porta Fisco and talk to a thug standing before the entrance to the sewers. He has a damaged umbrella which he will gladly give in exchange for something to eat. Roll up the inverter (it is found next to the cardboard boxes in the middle of the location) and visit Janosch's hideout to pick-up a canister and an empty pool (you need to perform the already described trick with dolphins). Make your way to the fortune teller tent and steal the bananas (you need to click on them three times before Rufus agrees to take them).
Travel to Floating Black Market. Enter the gadget shope and use the banana straightener. Once you leave the shop, talk to the fisherman. Ask him to fish out a shoe for you. The irritated man will tell Rufus that he won't fish until he is out of the area. Stand in a distance and do nothing until Goal starts to grumble and finally sneeze - the fisherman will surrender and give you the needed shoe. Give the shoe to a homeless man in Porta Fisco in exchange for the umbrella, then travel to the North Pole. Pick-up the rubber hose (next to the trawler) and travel to Watchit Island.
Travel to the tower, place the pool on the floor and ask Spunky Goal to stand in it - she won't agree, so change her into Baby Goal, who will happily conform. Click on the pump to fill the pool and give Goal the umbrella. Talk to her - you still lack one important factor - wood.
Return to the coast and take a look at the engine. Place the bananas at the exhaust, then connect the hose and the canister to the engine.
Return to Porta Fisco and enter the sewers. Take a look at the old turbine on the wall, open the tank and pour the gasoline from the canister. Place the energy inverter in the machine's hatch and press the blue button next to the door. The homeless man's smell will start pouring into Janosch's hideout. Enter the room and pick-up one of the air fresheners (in form of trees), and Rufus will do the rest. Return to Watchit Island and use the air fresheners on Goal. Give her the winning lottery ticket. Now, install the transmitter on the tower.