A real dungeon

sure we trust you

If you talk to everyone in the elf village you find someone who says something about a castle in the west. If you go there you find no one except some bats and a king who asks you to retrieve his crown that was stolen by Astos and hidden in the swamp cave. To progress with the plot you need to help this completely innocent king that I don't suspect for a second of anything bad (wink wink) and go into the swamp cave to the south.

worse than on Nickelodeon 

The swamp cave is the first real dungeon of the game. I know there is technically the temple of fiends but you won't be able to waltz in this dungeon and fight the boss the first door you enter. There are a lot of difficult monsters that can mess you up if you are not prepared. In particular I suggest you get the fira spell and the diara spell from the elf town (called fire2 and harm2 in the nes version) as well as plenty of potions and ways to deal with poison.

No you can't be king in this game.

There is some nice treasure in the swamp cave but nothing vital except for the crown. To reach the crown you need to go the downward path then go down the stairs. Then go to the bottom and to the right, enter the door and go out the door to the right. On the third floor there is sort of a grid. The room with the crown is on the third row down and the second column from the left. When you approach the chest you will fight some piscodemons. They can hit pretty hard so have high hp when you fight them.