I have backups scheduled in my laptop for a certain day and time. If the backup server is not available at the scheduled backup time, how do I ensure that Giga Vault Storage in my laptop runs the backup as soon as the backup server comes on?

Simply ensure that the " Attempt to run this backup every 5 minutes in case of non completion because of a problem (Network error etc.) " box is ticked when you configure the backup schedule. This option is part of the 'Advanced Options' that can be configured by clicking the 'Advanced Options' button under Step 5 (Scheduling) in the 'Backup-->Add Backup Schedule' menu.