Clear the game cache
Wipe Skyrim's install data from the HDD,
Wipe Dawnguard install data from the HDD
Clear the system cache
Then start over by installing the game, then patching to 1.6, then re-downloading dawngaurd from your download history. Start the game, go to the main menu and wait on it installing the dawnguard data. Once thats done try a new character and see how it goes.
If you still have a problem, then I would surmise that either xbox is going bad (hdd maybe) or your interent connection is spotty and/or has a noisey line causing data corruption with downloads.