It lets you use the same password again, but the username must be unique. Check that you're using the code linked to by Philo Kvetch and that the username query (around line 26 or 27) in register.php uses $username rather than &username.
The activation link must contain an id and a code parameter. The link sent by register.php should look something like "activate.php?id=4&code=25552321". If not, find where the link is output from register.php (line 76 on my copy) and make sure the line reads: