I keep getting sent to desktop around when alduin lands on the tower at the start of the game. I know it's caused by the HD dlc, because I tested it multiple times with and without the dlc, and it only crashes with the dlc, and always around the same time.

Are you using a 32bit operating system? The HD texture pack has in its requirements a 64bit OS, and using it with a 32bit version will cause crashes.