So are you sure it is installed correctly? It installs a bit like a mod in the respect that DLCShiveringIsles.esp needs to be activated. Have you tried reinstalling Shivering Isles?
Quest SE01Door starts the game enabled.
Here is a console code to get the quest message (and perhaps enable the island):
SetStage SE01Door 10
Here is a code to get another quest message and get the actor you will meet into position if you teleport into the gate using a console code.
Setstage SE01Door 20
Here is a console code to teleport inside the portal to the first room you would see in the Isles:
Player.MoveTo SETamrielDoorMapMarker
Hopefully there is something here that helps you. Try the earlier things on the list first. Shivering Isles is really amazing!
Good luck! I am sure there is some solution available.