I upgraded a Joomla site from 2.5.28 to 3.6.x. Everything seemed to go well until I went back to check on things. When I went to the site and began to click on various links, nothing worked. None of the menus were working after migrating either. After searching I found this post in the Joomla Support Forums about this issue and also this post.
As was stated in the support forum, if I turned off SEF and URL Rewrite in the Global Configurations and then the links worked. If I turned on Search Engine Friendly URLs (SEF) but turned off URL Rewrite, they worked. There is something wrong with URL Rewrite. Then I also saved the .htaccess to htaccess.old and created a new .htaccess file. Then I was able to turn on URL Rewrite again.