If you can't get at your html, don't switch hosts until you can get at your html. That's the meat and potatoes of your site (well at least the meat)...

You should contact the host to have them help you access your files.

Go here to Network Solutions and do a whois search.
Type your web domain in and you will be able to see who is in charge of your site. Contact them for assistance.

Once you have access to your files, download them to your computer. Then you will be free to change hosts.