Just had a simular situation on my machine....
Take a close look a BOTH icons...I'm sure you find that 1 is Internet Connect and the other is "Local Lan"
It's too simple really....Just go to the properties page of the Local Lan icon and remove the "showdesktop icon" checkbox.
There is no need to DISABLE either connection. (and strongly suggest that you don't)
I found the setting was activated by a settings change in another program.
Hope this helps...Let Me know plz?!!!