Broken links after database restored

I’m transferring my wp blog from powweb to bluehost. I had many problems copying the databases because bluehost runs an older version of phpmyadmin. Now I can’t seem to get the new installation to read normally (international characters not supported), and links to posts and comments are broken.

I really do need another way to copy the blog from one server to the other.
Do you know if bluehost allows you to have your own phpmyadmin installation?

Any ideas as to what I can do with this?