Either you are using the open_basedir parameter in a php.ini file somewhere on your site or your host is using that same restriction as part of the php setup for your account.
From what I'm reading in your attachment, the open_basedir command is restricting your installed applications to opening and reading files in four locations:
function_tempname appears to be trying to access 'upload_tmp_dir' which vB is translating to a path that is outside of those four paths and open_basedir doesn't like that. If you have cPanel access try searching for all existing php.ini files and find the 'open_basedir="...' command and try editing it to include your forum home, such as:
You may find the php.ini in any of the specified paths or if you have a VPS the open_basedir can be turned off entirely in the httpd.conf with the command
Code:
php_admin_value open_basedir off
This will make any php.ini open_basedir commands useless.