with the name of my existing database and the user and password i enter in phpmyadmin to come in, drupal doesn't go to the next step, but also it doesn't create any errormessage, just all fields are empty again. when i enter any adequate fantasy-names, it tells that this is the wrong password or username..why is that?
Hard to say. Can you ask your host support? Is there an error log to look at?
and what should i do now, especially in case i would love to avoid creating all nodes again - is there any possibility to recreate the nodes from the old database when i do a fresh-install and the backup is faulty?
Depends on the backup--if the data is there, then it's probably possible to re-instate it. May have to do it manually however, which can be difficult.