The geometric network needs to have a geometric network added to ArcMap to be active. It is not a licensed toolbar and has nothing to do with the Network Analyst extension. The Network Analyst extension works with Network Datasets primarily for transportation problems. The geometric network is for utility (electric, sewer, pipeline) type of applications and you use the Utility Network Analysis toolbar with them. Read more on them here:
Also, if you have done all this, make sure a layer is selected in the table of contents or a feature is selected so that you can use specific tools in the toolbar.