I would check php error logs, mysql error logs, and apache/iis logs.
I would also make sure that Admin panel -> Settings -> Bind Staff Session to IP is disabled. (You can toggle this at the mysql level by editing the database directly if you REALLY need to).
If all that fails, I would turn on error reporting:
If you can not find any solutions to the problem you are having, you can enable the "Show Errors" flags located in /main.inc.php:
#Don't display errors
ini_set('display_errors',0);
ini_set('display_startup_errors',0);
Change this to
error_reporting(E_ALL);
ini_set('display_errors',1);
ini_set('display_startup_errors',1);
Make sure that you turn it back off when your done.
after thought: I know that others have experienced this thing before. Searching the forums should also yield some additional help and maybe some resolutions.