Sounds like possible broken index.php, and since you just migrated, I'd bet the farm on an ill file transfer. Have you tried re-migration? If your templates are stored in the DB and not as files, it's possible you have a failed database migration (the template table may be corrupt), or if you save templates as files, your file could be corrupt.
Head on over to your
and look at index.html file. Can you paste it's template contents (you can remove most of the HTML elements or use pastebin to present it).
After checking out your template... It's behaving exactly like it's supposed to. If you're not logged in, all you should see is "is a guest". My first guess is that somehow your default template group got changed (do you have more than one template group?). If someone else did this migration for you, they screwed you on set up. From your pastebin, I would at least fix this line:
I'll be honest, this looks like somebody's test template, and not at all like the index page of any production website. You should really go back to your third party migration team and ask them what the hell they did, because that template is not the homepage of a production site. Is it possible your template folder originally lived as a git repo, and somehow a very old commit was checked out?
Member Group 3 is the Guests group. Have you tried logging (the Control Panel) and returning to your index page tosee if that page gives your channel entry loop?