does not load

I tried to modify your code, by putting in ~/tmp as the temp path, which helped remove the MODULE errors.
and by putting in absolute path to the .php files referred.

Now, I get the following error:
Fatal error: Unknown function: backup_form_backup() in /var/www/vhosts/mina.ubc.ca/httpdocs/drupal/modules/backup/backup.module on line 82

Next, putting in the absolute paths, and by cutting and pasting all the .php functions into the .module file, I had a little more success, but still many errors:

warning: backup_form() [function.backup-form]: open_basedir restriction in effect. File(/usr/share/pear/forms.inc.php) is not within the allowed path(s): (/var/www/vhosts/mina.ubc.ca/httpdocs:/tmp) in /var/www/vhosts/mina.ubc.ca/httpdocs/drupal/modules/backup/backup.module on line 78.
warning: backup_form(forms.inc.php) [function.backup-form]: failed to open stream: Operation not permitted in /var/www/vhosts/mina.ubc.ca/httpdocs/drupal/modules/backup/backup.module on line 78.
warning: backup_form() [function.backup-form]: open_basedir restriction in effect. File(/usr/share/pear/forms.inc.php) is not within the allowed path(s): (/var/www/vhosts/mina.ubc.ca/httpdocs:/tmp) in /var/www/vhosts/mina.ubc.ca/httpdocs/drupal/modules/backup/backup.module on line 78.
warning: backup_form(forms.inc.php) [function.backup-form]: failed to open stream: Operation not permitted in /var/www/vhosts/mina.ubc.ca/httpdocs/drupal/modules/backup/backup.module on line 78.
warning: backup_form() [function.include]: Failed opening 'forms.inc.php' for inclusion (include_path='.:/usr/share/pear') in /var/www/vhosts/mina.ubc.ca/httpdocs/drupal/modules/backup/backup.module on line 78.
System program "mysqldump" not found in $PATH. Please check with your sysadmin for further assistance.
warning: backup_form_files() [function.backup-form-files]: open_basedir restriction in effect. File(/usr/share/pear/functions.inc.php) is not within the allowed path(s): (/var/www/vhosts/mina.ubc.ca/httpdocs:/tmp) in /var/www/vhosts/mina.ubc.ca/httpdocs/drupal/modules/backup/backup.module on line 626.
warning: backup_form_files(functions.inc.php) [function.backup-form-files]: failed to open stream: Operation not permitted in /var/www/vhosts/mina.ubc.ca/httpdocs/drupal/modules/backup/backup.module on line 626.
warning: backup_form_files() [function.include]: Failed opening 'functions.inc.php' for inclusion (include_path='.:/usr/share/pear') in /var/www/vhosts/mina.ubc.ca/httpdocs/drupal/modules/backup/backup.module on line 626.