Re: The requested URL /groups/ was not found on this server.
other than the check for mod_rewrite.c, you have the same .htaccess that I have in a default install, with permalinks set to /%category%/%postname%/ (http://playground.21inspired.com is a simple default install).
My .htaccess:
# BEGIN WordPress
RewriteEngine On
RewriteBase /
RewriteRule ^index.php$ – [L]
RewriteCond %{REQUEST_FILENAME} !-f
RewriteCond %{REQUEST_FILENAME} !-d
RewriteRule . /index.php [L]
# END WordPress
Unfortunately, this is beyond my area of expertise. Hopefully, someone else can help you get rid of index.php in your urls, and get the blog & BuddyPress urls resolved correctly.
Other quick thoughts: is your .htaccess in your site’s root directory? Do you have other .htaccess files in the subdirectories? Does your server support mod_rewrite?
Anyone able to help?