cPanel import is in beta, so I understand people have problems. As I said, I couldn't get my databases to import.
Really, the simplest way would be to copy your public_html folder in your cPanel installation to the site folder on DreamHost. Then use the Wiki to check how to create a MySQL dump and import into a new database in DreamHost. It's a pretty trivial process really. You don't just copy the folder that contains your database files.
Having worked extensively with cPanel servers, I'd be happy to guide you further.