This at solved my problem (although I think there are many reasons for login problems with Drupal).
Using MySQL5 I ran this statement in phpMyAdmin
Then deleted the entire installation (including the tables of the database) and re-installed using the steps in the Drupal Howto with 4.7.6 (instead of 4.7.3)
It worked great.
I understand you can also add this to the my.cnf file:
but I am not sure how that works.
I found this solution in this thread at drupal.org http://drupal.org/node/42927