If you're having trouble with figuring out quests, go to Pie's Quest Guide
, search (Ctrl+F) for the name of the quest you have, and see what information it can provide.
To get into Dark Moon Castle, you need Ignite and Broad Jump. Finish the "Parabola in the Blue Sky" quest by digging flint in the Underworld Cave to get Ignite, and finish "Doo Da Da Jump!" by digging the two diaries in Mountain Cave 2 for Broad Jump.
Once you have access to Dark Moon Castle, the quests there should help you progress further.