I too had had trouble getting my Logitech device (MX700 cordless optical mouse) to recognized by LCC 2.1.2 under Mac OS 10.4.8 on a 2001 Quicksilver. I eventually got the mouse to be recognized, but then had several crashes of the Device manager while trying to configure it.
This worked for me:
Using the LCC 2.1.2 installer, uninstall v2.1.2
Restart
Install version 2.1.1 (http://www.logitech.com/pub/techsupport/mouse/mac/lcc211.dmg)
Restart
If you have more than one User, don't use fast switching, but shut down and log on as the second user before trying to configure the second user.
[Version 2.1.2]
Please login or create a new MacUpdate Member account to use this feature
Logitech Control Center
This worked for me:
Using the LCC 2.1.2 installer, uninstall v2.1.2
Restart
Install version 2.1.1 (http://www.logitech.com/pub/techsupport/mouse/mac/lcc211.dmg)
Restart
If you have more than one User, don't use fast switching, but shut down and log on as the second user before trying to configure the second user.