I did this by accident and it flummoxed me for a few hours
I got "Disconnected" While I was surfing and updating at the Same time in the Tool tray next to the Clock
Had my
Voyager BB modem showing Power On, No DSL Light!
Checked the wiring all OK
My Netgear Router was connecting up So I continued surfing with that
I returned later to the Problem.Reinstalled the Drivers...Still no Joy! Power light on ...No DSL light...Modem Failed? and out of curiosity I clicked on the Local area Connection Link and Discovered it was Disabled I must have Brushed the Disable link when I was updating earlier! I clicked the Enable link and the Modem Lit up again!
You can disable both the router and modem Connections in this manner if you are going away, and if it puzzled me for a while then a Novice will have not a clue especially if they want to sneak online or mess about

Any delay to Prying Eyes is a good thing
And you don't need to set a password for this
PS Link cannot be reenabled on the Desktop (only disabled) Must go to the Network Connections Folder to reactivate OK?

NOTE: Only works When the Item is Disabled (connected up) if you can still connect up then you've done it in the wrong order OK?