Try the following to be sure things are set up as wanted..
-Unlock the Taskbar with a right-click in a blank area on it.
-Right-click a blank area again, but this time, select Properties
-In the resulting dialog box, click on "Customize in lower-right.
-In next dialog box, what is to the right of the connection icon (two
monitors) ? If not "Always show", click on it or the connections name to
highlight and get a box around the status with an inverted triangle to the
-Click on triangle, then click on "Always show"
-OK, Apply, and OK to close
-Lock the Taskbar with another right-click in blank area.
This should have the Dial up icon always available by the clock. If it
isn't, I defer to the more expert.