Hint: When you arm your sword, you'll be able to use the ice ball magic.
Go near the castle entrance (west of here), then talk to the guard. Ask him to let you in. You must now beat him in puzzling. Answer DRAGONS, then ask him what a diary is. Go north, talk to the king. Accept the task. Now exit the castle and go talk to the fairy. She's northeast of here. She will ask you to find her necklace. Ask her where she saw it last time. Go near the castle entrance and go southwest to find the forest entrance. Southeast of PillEr forest is a machine. Use it. Save your game if you want and push the button. Go to the southeast corner of the island now. Pick up the necklace, go back to the machine, push the button. It will teleport you to an island. Enter the house north of here. Talk to the man. He wants you to look for someone who will fix a bridge. Look for an old lady who lives in a house near here. Talk to her, then go upstairs. Go back downstairs and talk to her again. Feel free to explore the island a bit more if you want (you can find a wizard who can teach you the hellfire magic), then go back to the guy who has a boat. Talk to him. Now that the bridge is fixed, he will take you back to Grandland. Now go back to the fairy Bincabbi, talk to her, and this is the (surprising) end. Congratulations, you've finished The Fairy Named Bincabbi.