You DO NOT want any Red X on that bottom left phone icon. And that bottom left phone icon should always be set to use my Computer for phone calls. What can fix a lot of issues is Signing Out, go to the Gear in the upper right corner and sign out. Aslo Exit Jabber from the Task Bar under Show Hidden Icons.
After completely exiting, Open back up Jabber and click the Reset Jabber toward bottom of screen. Login will come up, firstname.last@gcisd.net and then firstname.lastname. See if that clears it up.