The king is dead, I have the amulet, the kings guard gave me a key, and I go to the locked steel door and it says it takes a key and that is it. Checked all the dead assassins, no help there.

How do I get through the door and into the sewer.

You don't go through the steel door, you go through the opening next to the Emperor.
See pic

I tried that first and was blocked. I will try again.

That's strange. If that's true it sounds like it could be a mesh bug, the game thinks there's still an obstacle there when in fact there isn't.

Please clarify: You walked to that opening in the wall and you were blocked, just like by invisible walls? I don't remember that scene exactly, but perhaps you have to jump (unlikely, but you have to consider all possibilities)? Is it possible that you missed a certain conversation with the Emperor? Have you received the amulet and the associated quest from the Emperor (you said you have, but better double-check, including the quest list)?

As you are still very early in the game, I suggest you simply start a new game, and if the problem re-appears, then I would consider un- and re-installing the game. Or downloading an end-of-sewer save game where you can review (and repeat) the whole character creation process.

I was stuck because I did not hit the "E" key to raise me up a few inches so I could get through. It is a small door and if you are a bit high you are blocked too.

Anyway got through.