I've had your problem too until 10 minutes ago
Clementine uses libgio or DeviceKit (which is split in several modules, like udisks) to connect to the devices.
libgio comes already with the glib package on Slackware 13.37, so Clementine picks it automatically during configuration phase, but, be it either an old gio version or an incomplete implementation on Clementine's side, the thing doesn't work and devices do not get detected.
I compiled and installed udisks (and its dependencies), recompiled and reinstalled Clementine and now it works flawlessly.
I just tested connecting a USB disk drive and my iPod nano 3G and both work.
You can find udisks and dependencies on slackbuilds.org. Remember to rebuild Clementine too after installing udisks.