Fixed! I installed DirectX 9 straight from the Microsoft website. That did the job.
I'm having odd graphical errors and can't start a game as well. I get the loading screen, then the first time it went to a black screen. I could hear music in the background, but nothing is showing on screen. I tried re-installing DirectX and even re-downloaded it from Microsoft. Every time DirctX tries to install it says the version I have is the same or better than it is and it won't re-install. I tried launching the game again, got past the loading screen, and then it went to a white screen. I could hear music, but nothing was showing on screen. This time I opened the task manager and it said Skyrim had stopped responding.
Please help! Any thoughts would be greatly appreciated as I'm dying to play it after getting home an hour ago from the midnight release here.