I solved the problem. Probably in the most inelegant way but it worked.
(Maybe there is someone out here who is able to translate my description in a serious a´posting. I really have no idea of that whole 'programming' thing. hahahaah.)
Instead of checking and changing the table_prefix inside the config.php I tried changing all prefixes in SQL.
In detail: I imported the sql from WP Migrate DB to my database and named these files like WP did it whilst the fresh installation. It also took me long time to find all meta_keys entries in _usermeta, _postmeta, etc. But then, when I changed everything my login worked again.
Hope I could make it clear.
Best.