OK, just in case somebody else runs into this problem: Apparently Mysql recently adopted a stricter policy, so that values are not null by default. The (almost) solution for me was to remove the "STRICT_TRANS_TABLES" from the my.cnf file. Before that, the display_name was undefined and it threw an error (which was displayed in white on white ...).
Now I got the "almost installed successfully message", with no code to copy and paste into the index.php. After that, I haven't gotten it to work. I tried also copying the site.php from a successful install (and editing the included information), but when I try to log in, it says that the username was not found.