I have already killed the master vampire before I started this quest. Now I am at the part where I have to enter the cave to kill the master vampire but I just get stuck in the loading screen. Am I screwed?

Yup. Not sure what you can do. If you're on PC, likely you can fix with console entry. Otherwise.... svcks.

Wow, talk about lazy script writing. How about a simple line that says 'I already killed him"? It worked for the dragonstone that I found before I was sent on that mission. Still can't believe this game won game of the year.

• If you enter and clear the dungeon before begining the quest, Morvath will be replaced with a generic "Master Vampire".

This is what it states in the UESP

http://www.uesp.net/wiki/Skyrim:Laid_to_Rest

Avinar, I know what it says. It didn't work that way for my first toon.

That information is wrong. This quest can not be completed if you kill him before starting the quest.