Q: Can't backup my new ipad mini

Make sure you have it connected to wifi and your charger, and that the screen is locked.  If it still won't back up, it could be caused by a corrupt existing backup that needs to be deleted, or by data on your device that is preventing the backup from succeeding.  To troubleshoot these, try deleting your last iCloud backup (if you have one) by turning off iCloud Backup in Settings>iCloud>Storage & Backup, then tap Manage Storage, swipe across your backup and tap Delete, then go back and turn iCloud Backup back on and try backing up again.

If it still won't back up (or you don't have an existing backup to delete), you may have an app that is preventing the backup from succeeding.  To locate which one, go to Settings>iCloud>Storage & Backup>Manage Storage, tap the name of your device under Backups, under Backup Options tap Show All Apps, then turn them all to Off (including camera roll) and try backing up again.  If it succeeds, then the camera roll and/or one of your apps is preventing the backup and you'll have to located by process of elimination. Turn the camera roll On and try backing up again.  If it succeeds, turn some of your apps to On and try backing up again.  If it succeeds again, turn some more apps to On then try again; repeat this process until it fails.  Eventually you'll be able to locate the problem app and exclude it from your backup.