Did you also change domain names, or maybe change the path to your blog? Changing hosts should not cause any problem if you have the same domain name and path.

Anyway unless you have hard-coded stuff in your files you shouldn't need to change any files other than conf/_basic_config.php, and you probably know if you added stuff to files that includes links. That means you have to look to your database for where the problems are. There is a way to tell a database to update all instances of 'foo.com' to 'bar.com' but I do not have a link to that info anymore. Bummer for me because I know one day I'll need it, but you could still do it manually by using phpmyadmin to find all cases where the wrong path is, then change it to the new path.