I recently reinstalled Skyrim with no mods to get a fresh start, and when I load up the game it will not let me start a new game, as it crashes after showing the little statue of Alduin for a few seconds. It doesn't CTD, it just freezes on the screen with Alduin and I can hear horses panting in the background as if the cutscene is about to start playing but it never does.

What changes in the hardware have you made since it ran last? Maybe you need to let it generate a new INI? (That is, assuming you held onto some saved games.)

I removed all saved games, but I think I found the problem. I used to run the game on max settings, but for some reason I can't anymore even though I haven't changed any hardware and I've tried my old GPU drivers and the latest ones.

I found out that I can max everything except for Ultra shadows, as that somehow prevents my new game from launching, so I have to play with High shadows. Is there a known problem with this?