Do you have any databases? Don't forget those bad boys.. another reason to get your new host to do it. I've never had a host say no, or try to charge me for it. I just told them the domains, what software was being used, and gave them my credentials for the old server/virtual.
Move to techiemedia.com and they'll happily move your stuff in about 20 minutes, and make sure your DNS is set up properly
