None of the previous solutions solved my problem with the same symptoms. But after much hair-pulling I discovered that the wp-settings.php file had NOT been written over by the new 2.6.2 version. So I updated that file with new 2.6.2 version of the file and voila – no more blank page on the site and no more looping on the login page. So, another possible cause of the blank page/login loop issue is a missing or non-updated file. So be sure to go through your 2.6.2 update and check to make sure that ALL the necessary files outside the wp-content folder were actually updated.