The name entry in variable table is supposed to be maintenance_mode following updates in D7 after which site_offline and site_offline_message were replaced with maintenance_mode and maintenance_mode_message. Refer the inline comments in update_fix_d7_requirements in update.inc

  // Rename 'site_offline_message' variable to 'maintenance_mode_message'
  // and 'site_offline' variable to 'maintenance_mode'.
  // Old variable is removed in update for system.module, see
  // system_update_7072().

Assuming you have access to the database or drush try updating the variable which is likely set as 1 to 0.

drush vset maintenance_mode 0

or

UPDATE variable SET value = 's:1:"0";' WHERE name= 'maintenance_mode';

Many users with similar issue also suggest even clearing the cache table entries named variables for this to work after changing the variable value. If things go well this should bring your site back online.

The name entry in variable table is supposed to be maintenance_mode following updates in D7 after which site_offline and site_offline_message were replaced with maintenance_mode and maintenance_mode_message. Refer the inline comments in update_fix_d7_requirements in update.inc

  // Rename 'site_offline_message' variable to 'maintenance_mode_message'
  // and 'site_offline' variable to 'maintenance_mode'.
  // Old variable is removed in update for system.module, see
  // system_update_7072().

Assuming you have access to the database or drush try updating the variable which is likely set as 1 to 0.

drush vset maintenance_mode 0

or

UPDATE variable SET value = 's:1:"0";' WHERE name= 'maintenance_mode';

You might also want to ensure that this value is not set as 1 with a $conf variable in your site's settings.php. Many users with similar issue also suggest even clearing the cache table entries named variables for this to work after changing the variable value. If things go well this should bring your site back online.