It stops @ Downloading install package from https://downloads.wordpress.org/plugin/buddypress.1.8.zip…
Unpacking the package…
How do I upload buddypress?
you can download the zip file extract it then upload via ftp to your plugins folder.
@parmkals
As @ubernaut stated I would FTP BuddyPress because if you do not have access to the php.ini then you can not change it and it may hang when downloading and installing BP. If that is the case then just download BP to your hard drive extract it and FTP it to: your-site/wp-content/plugins on your server. You will need the credentials from the server to do this and that is something only you can acquire. I supplied a link that will hopefully help you get started if your not familiar with this process. Good luck!
https://codex.wordpress.org/Using_FileZilla
