To bounce off of what calistoy just said, you should try doing what it says and moving the contents of your IPB install to the public_html folder of your site manually via FTP or File Manager. For more help on this, you should try contacting SMF support.
Here's why open_basedir is enabled: open_basedir prevents you from accessing files outside of specific directories from within your scripts. For example, without this restriction, other people on the same server would be able to access your account's files, which I'm sure you wouldn't want happening. Unfortunately, it seems the SMF script is too stupid to realize that your home directory is actually INCLUDED in the list of allowed directories, so it just quits anyway even though it would easily succeed if it tried.