From inside the ship, go left into the storage area. Pick up the shovel. Notice a wooden box behind a loose board on the bottom right of the screen. Click the board to reveal the box. Pick up the box and click on the cover. Notice that it won't open. Put down the box and go back. Go right to the other storage area and pick up the 9V battery on the floor. Go back and exit the ship.
Go back inside the hut and pick up the metal detector. Grab the 9V battery from the inventory. Insert the battery into the metal detector batter door. Press the red power button. Pick up the metal detector to add to the inventory. Exit the hut.
Go back to the outside of the hut and follow the trail on the right. Outside the cave, notice that there is a roman numeral XI there. Go inside the cave and notice that you can't see anything then exit the cave. Outside the cave, grab the metal detector from the inventory. Move it around the sand until it starts to glow yellow and you hear a blaring siren sound. Put down the metal detector. Grab the shovel from the inventory and move it over to the place where the metal detector indicated. When the shovel glows yellow, click to dig a hole. Notice that a key is revealed. Pick up the key.
Go back into the ship and pick up the wooden box. Grab the key from the inventory and place it over the lock on the box until it glows yellow. Click to unlock. Open the lid. Pick up the magnifying glass. Pick up the piece of paper. Put down the box and exit the ship.
Go to the outside of the cave. Go left to the firepit. Grab the palm branch from the inventory and place it into the firepit. Grab the magnifying glass from the inventory and hover it over the palm branch until it glows yellow. Keep it there until the branch catches on fire. Put down the magnifying glass. Grab the lantern from the inventory and hover it over the fire until it lights up.
Go into the cave and pick up the green tube on the right side. Grab the green tube from the inventory. Grab the paper from the inventory and move it anywhere over the tube and click to insert it. Notice that you can scroll the paper in the tube up and down by clicking on the black handle on the right side. Scroll the paper until the number in the left box is correct.
If you're having trouble figuring out which number is correct: Remember the roman numeral XI outside the cave. It is the number 11. Scroll the paper in the tube until the number in the left window is 11.
Put down the tube. Look at the cave and notice that it looks like an animal. Grab the tube from the inventory and find a picture of the animal and notice the arrow to the right of it. Use that arrow to determine which path you should follow in the cave. Repeat until you find the exit.
If you're still having trouble finding the cave exit: Further into the cave, the openings start looking like two animals fused together. Ex. Left half goat, right half owl. Don't let this confuse you. Just look for the corresponding picture in the tube and determine which opening to take.