This has been covered numerous times in other threads on the forums.
You might want to turn off Admin panel -> Settings -> Bind Staff Session to IP. I realize that you cannot log in to do this, however you should be able to access the database via PHPMyAdmin or CLI or some other 3rd party application. To shut this off manually you can either access the ost_config table via one of these applications and change staff_ip_binding to 0. Or run the following snippet of MySQL Code:
UPDATE ost_config SET staff_ip_binding = '0' WHERE id = '1';
You might also find this post helpful (scroll down to munchkinman's post)
http://osticket.com/forums/showthread.php?t=1386(http://osticket.com/forums/showthread.php?t=1386)
You might also want to take a look at your PHP log and let us know if you see any errors in it.