how are you exporting you database. My advice is to use a current version of phpMyAdmin some of the older versions had some real bugs in them and cause flakey results. On the new site make sure the database is created but no tables and import it in. It should work like a charm.

If you think it's a problem with the db names then check to make sure your configuration is correct.

Column 'group_id' cannot be null

The index cannot have a null value that's what that error means (assuming group_id is the index)