More information: TDE handles a HAL eject and a TDEHWLib eject the exact same way, via a call to kdeeject, which then calls eject. As eject used to rely on HAL, I would not be a bit surprised if the 'eject' binary is broken on Slackware 14 (the ioctl errors would support this hypothesis).
At this point I don't think eject is broken. As mentioned in a previous post, eject and icon disappearance is working on Slackware 14 with Xfce 4.10 and KDE 4.8.5. More, Slackware 14 is being heavily tested by many people and nobody is reporting breakage with eject.
Can you try using kdeeject from the command line on your CD drive to see if it works at all?
Thanks!
Tim