BuddyPress.org

first did you deactivate plugins and change theme to rule those out?

if you are comfortable access a database and editing php search here on the forums, there was a previous issue where a db column was missing. but that issue was a while ago.

Are you on multisite? also did you use a one click WordPress installer that a web host provides?

so you didn’t download wp and install? Hostgator is notorious for borked WP install from their interface

You said you installed WP from hostgator? Did you create a database manually, use FTP to upload WP or did you log into hostgator admin and click a button to install WP?

is this site already active with users? You might need to reinstall everything fresh.

Read this thread, its probably the same issue, has some suggestions. https://buddypress.org/support/topic/new-user-registration-problem-invalid-activation-key/