I'm playing the demo version. Anyone know if I purchase the full version, can I continue playing my character and story from the demo, or do I have to start over?
It continues where you were. The demo is actually the whole game with the rest locked up.
But... Bear in mind it seems to save when you go through portals.
At the end of the demo (the original one anyway) there was option to go down stairs or through a town portal. Clicking on the stairs it took me out of the game and when I loaded I was right back when I last travelled through a portal. This isn't really a biggie but I did lose a particularly nice piece of loot.
I should caveat that I guess it's possible this actually happened due to an issue fixed in the recent patch.