What I have done to fix it.
Edited the /etc/mysql/my.cnf file. I have added
. Restarted the mysql server
I now was able to get into mysql without login and password. I imported the backupped mysql.user table. Deleted the "skip-grant-tables" from the my.cnf file. Rebooted the server and everyting was fine again. Phoeffffff.
Another question now. What should I delete from the mysql.user table. I know now not the whole table.