Ok, then 'none' is not what you are looking to do. 'None' would imply no access to any directories.
The error you are getting is telling us that you need to ADD the following:
/home/httpd/vhosts/giftbasketdepot.com/httpdocs/install
to the existing open_basedir statement, which is:
/home/httpd/vhosts/giftbasketdepot.com/httpdocs:/tmp
So try putting (in /etc/php.ini):
open_basedir /home/httpd/vhosts/giftbasketdepot.com/httpdocs:/home/httpd/vhosts/giftbasketdepot.com/httpdocs/install:/tmp
all on one line, no line breaks (be careful with nano, i have seen it write line breaks where you didn't put one; also seen vi do it).
Order of priority precedence for php directives:
Domain vhost.conf or vhost_ssl.conf
Domain httpd.include
Apache httpd.include
Apache httpd.conf
/etc/php.ini
This means that if you have open_basedir in the php.ini file, and also in the domain httpd.include, the one in the httpd.include will take priority and the one in the php.ini will be ignored.
If you have open_basedir set in the vhost.conf file, and in the domain httpd.include, and in the php.ini (all 3 different), then the one in the vhost.conf file will be the 'effective' one, the other 2 will be ignored.