My hosting troubles are over. I hope. The switch was really easy and happened really quickly. I registered, moved my files, downloaded my SQL from my old site, imported it into my new site and voila! Everything worked. The nameservers took only hours, too. My email client works without anything more than updating the password.
After the DNS change, I searched for a way to contact my old host. Their site is like a ghost ship. Most of the links do not work. There's nothing in the knowledge base. Nothing in the forums. I found an email with a link to log in to a secure area for updating my credit card info. I put in a fake credit card number. I found an address in there and wrote a letter and sent it via snail mail to officially cancel my service. I attempted to use their system to send an email but it bounced. If I owe them any money, let them send me a letter via snail mail and then I'll have their real contact information, if it exists.
How did it come to this? When I signed up they were great. I could call their sales line and get the same guy that did the tech support. He would help me instantly right over the phone. I guess he sold his company to someone else. It almost seems like this company wants people to leave.
Let's hope my efforts were good enough to be done with it.