Like if it is being hosted on another host under another domain name that you've never heard of, let alone given permission to, here's what Vertical Response did, who is a major and trusted enewsletter provider:
You need to be a sleuth. Quiet and stealth-like as you backtrack.
First, check the WHOIS Directory. This tells you who owns a domain, the domain that is hosting your stolen site. Or even if they are hotlinking (aka robbing you of your images while sucking your bandwidth), you can check here for some clues. This can be made private, and numbers can be falsified, so it's a chance.
If an email was involved, like with Vertical Response, see if you can track the IP address who sent it, or call your host or enewsletter provider to see if they can help you track it down.
If there is a phone number or any type of contact information, use it. But be nice. They could suddenly dissapear.
Oh, and to get tipped off that this actually happened, set up a Google News Alert for your domain name and see what people are saying about you. Or try Andiamo Systems which is another system, but I've never tried it.
ps: If your website has been stolen, tells us about it via Comments!
pps: hi Vertical Response! I know you just Andiamoed this article. :)