I've managed to get ArcMap 10.1 trial installed and working, but I want to use Network Analyst and it says that this is not authorized. However, License Manager says that all extensions are authorized. See screenshots.
Licensed but disabled by default, so in ArcMap or ArcCatalog --> Customize there is an Extensions panel with a checkbox list of all installed extensions. Just check Network Analyst to activate and consume the license that you have.
Off by default because the state of the active extenstions gets recorded into the configuration files for each map. And also, in a networked license environment, you don't want to consume licenses that others could use just because of a default setting.