The screen shot you show is the first step to adding an activity. Do all teachers/users get that same screen or just your account? Either way, site is confused. Server running any cacheing like memcache(d) or any PHP op like APC or Zend OpCache?
Think I'd set sessions to use file rather than DB in config.php
$CFG->dbsessions='0';
A 'sessions' folder should be created in moodledata and one should see session files created as users login.
No need to restart services just access via browser. Before doing that, however, clear browser cookies and cache. And would manually clear the caches on Moodle as well:
cd moodlecode/admin/cli/
/pathto/php purge_caches.php [ENTER]
If one cannot use command line php one could try going directly via browser without logging on:
http://yoursite/admin/purgecaches.php
If that doesn't work, think I'd go to /moodledata/cache/cachestore_file/default_application and manually remove all the folders/files there. Moodle should re-create them.
And there are not clues/hints in any server logs for apache? error_log? does access_log show access?
'spirit of sharing', Ken