Some versions of BuddyPress require a specific version of WordPress. So if you’re using an old version of WordPress (you should upgrade that asap, obviously), you need to use the version of BuddyPress that last supported that version of WordPress.
Gosh. Why do you have that load wp-config.php bit at the top of the file? That’s a big red flag immediately. Are you doing something unusual to include this file into your site?
Changing the chmod of wp-content to 777 won’t actually *break* your site, but maybe something else happened at the same time. I’d suggest popping into the multisite forums at WordPress.org, and searching/asking for anything similar.
I’m not aware that BuddyPress uses a significant amount of CPU. From what they’ve told you, seems like they provide total bare minimum, low-end hosting. In all seriousness, I’d consider finding a different (better) host.
Are you trying to delete the group forums because a) you don’t want to use forum functionality on your site, or, b) you want to delete all the forums so it recreates new empty forums for you?
Do you know how to check your web browser’s console for any javascript errors or warnings? This is usually some other’s plugin’s javascript loading at the wrong time, breaking BuddyPress.
You could either download the 1.5 branch version of BuddyPress from SVN (https://buddypress.svn.wordpress.org/branches/1.5/ which *should* be stable enough to use in production, or try to make the relevant code change in your version of BuddyPress.
