It all depends on what’s happening here.
Could you go into your wp-config.php file and look for the line
define('WP_DEBUG', false);
Make sure this is set to true.
Re-visit your activation page and post the last error message you see (if any).
Also, in your BuddyPress theme could you find the file located here
wp-content/themes/your-theme/registration/activate.php
and post the code that’s within it please.