You could try changing this setting to blank ... just remove the letters: db
Code:
define('STORE_SESSIONS', '');
That will force it to do session-storage to the filesystem instead of the database. This is less versatile and somewhat less secure, but might reveal something if symptoms change.
What version of PHP is on your server?
You might try asking your host what PHP components have been changed on the server since it was last working properly for you.
Who is your host?
Do you have access to another webserver anywhere to use as a test ... to rule out your own equipment?