Remember that in Linux or Windows if you do NOT start with a / as the front of the path name the file or path are related to the current path. To insure you have the correct path name you should NOT assume you are starting in the right path and need to enter this into your paths.
Not knowing your site setup it is likely the web user account is starting in its "home" directory so what you list is not going to work.
Assuming the WWW home directory is actually:
/home/www/
Then your actual pathnames as you have them entered would be:
define('XOOPS_ROOT_PATH', '/home/www/');
define('XOOPS_PATH', '/home/www/xoops_lib');
define('XOOPS_VAR_PATH', 'home/xoops_cache');
So this is probably not what you want.
Assuming your main directory is / you would need to put that in your configuration like this:
define('XOOPS_ROOT_PATH', '/');
define('XOOPS_PATH', '/xoops_lib');
define('XOOPS_VAR_PATH', '/xoops_cache');
Just make sure that you use the absolute file path to your website in these lines. Which means on Linux it needs to start with / or with windows it might be something like C:\www
Beyond that you should NEVER use /root or / as a webserver accessible directory. This is extremly insecure and allows anyone accessing the site through the webserver to access any of the subdirectories if the site security is bypassed.
Your error is telling you where it is looking for your site.
Your main site should be in the directory:
/var/www/html/
So if you copy your files to that directory and then make sure you change your main file entries to match you should be set. You will need to also delete all of the files in your cache directories (Other than index.html) and you may need to delete all of the entries in the sessions table or you will have issues because the file paths have changed.
SO in other words your mainfile should have lines like this in it:
define('XOOPS_ROOT_PATH', '/var/www/html/');
define('XOOPS_PATH', '/var/www/html/xoops_lib');
define('XOOPS_VAR_PATH', '/var/www/html/xoops_cache');
