The current version of HPLIP, 3.12.10a, fixes the problem of the unresponsive HP icon.
You can download the tar package at http://hplipopensource.com/hplip-web/gethplip.html
(look for the link to the tar package) and build a Slackware package using the hplip.SlackBuild
file from your distribution disks' source directory then do an upgradepkg hplip*.t?z
Note that you will get messages if you log in as root and startx
; the HP icon will not appear in the task bar (it's not supposed to).
Hope this helps some.