Hello again!
Solve the problem!
The point was, that things didn't work well with compiled versions.
After turning on the non-root mode, I had to manually add the CD devices. I used /dev/hdc and /dev/hdd.
It all worked well while I was loged as root, but no chance in user mode.
When I used the RPMs from Fedora Core 3, xcdroast did mention that root password would be needed for nonprivileged user to start, but it didn't.
The non-root mode is not there, but all works well for non-privileged user. No root password needed.
Si I have to correct myself - IT WORKS!
And thank you Alexander for that list of your installed RPMs.
Davor.