Okay, crap. Found out that the account I had logged into was the account I'd had years back for my trial period when testing it out. My OTHER account, the one I'd made when actually starting, was the one that got hacked into. So they didn't actually move the character, but they switched my account to a different email address.
What's worse [and it didn't occur to me that this might be related] is that Gmail gave me a message that it thought someone might be messing with my account and asked me to change my emails. So what the person might have done was take my account and then go into my email and delete all traces of messages from blizzard from my gmail account before I changed the passwords.
Ug, this crap sucks big time. I know it's only about a game, but if it's my email too... that's just really annoying.