You cannot enter the dungeon cell from the castle library, but you can go through the back gate which is opened by the switch. A tunnel leads to Mordred's secret underground laboratory.
To get the key to Mordred's laboratory:
Inside, you just have to push down the dirt wall to enter the passage.
The cell is only "blocked" by the bars on the dungeon side. When you throw the switch, it opens the back gate, which leads to Mordred's underground lab. (see related question)
The coordinates are X 11, Y 82
Once the Golden Key and the Green Orb are returned to Arturus, there is no way to open the crystal gate.
There is no way into the cell from the library. Throwing the switch opens the "back gate" to the cell, which you can access from Mordred's underground laboratory. (see related question)
To draw the sword from the crystal stone, you must have defeated all three planets (jungle, ice, and fire) and have all three knights with you. (see the related questions)
Feed the mouse to Merlin, the mechanical owl, and he will follow you into the cell. Click Merlin, then the vial, and he will retrieve the fuel rod for you.
When you first enter the dungeon, you get the cheese and throw the switch that opens the back gate on the dungeon. (if you didn't, go back and do it) When you enter Morderd's secret underground lab, the wall to your left is just dirt, and you can push right through it.
The small gate is in the BACK of the dungeon cell, and connects to the tunnel Mordred dug. By throwing the dungeon switch, you open the gate so you can come in that way. (see related question : getting back in the dungeon)
In the dungeon under the castle library, pick up the cheese and pull the switch that opens the back gate of the cell. In Mordred's underground lab, once you feed the mouse to the owl, you can go down the passageway to the cell gate. Next to the bars, the wall is dirt and you can just push it down.
There are many doors on Astro Knights island, but none appear to be blocked. The gate to the dungeon cell is opened with the switch when you enter through the library. The underground lab is opened with the small key (from under the village fountain). The dirt wall is easily knocked down to access the back of the dungeon cell. Later in the game, the Golden Key must be drawn and the cards must be turned to open the entrance to Mordred's castle. (see related questions)
you fly to a large asteroid in the asteroid belt and land there. that is the crystal gate when you climb to the top
Go back down and pull it. You need the gate open to reach the cell. (see the related question)