If you cannot use extensions, such as Spatial Analyst or 3d Analyst, make sure they are turned on by going to Customize >> Extensions.
If you cannot connect to a PostGreSQL database, make sure these DLL's are installed: PostgreSQLClientLibs.zip
If your basic interface is messed up, for example, if a menu appears far away from where you click, make sure your Windows Display Settings are set to "medium (default)". This happens especially with 4k monitors.
ArcGIS Desktop does not play well on 4k monitors with certain video cards. If ArcGIS Desktop crashes when your window is full-screen or larger than 2000 pixels wide, try lowering your display resolution to 1920x1080 or smaller.