You can perform a manual backup using iTunes on your computer even if your are automatically backing up to iCloud. To do this, connect your phone to iTunes, then right-click on the name of your phone on the left side of iTunes and choose Back Up. You should also sync your phone to transfer any purchased apps and media to your iTunes library, and sync your contacts and calendar with iCloud so they are backed up separately (Settings>iCloud>Contacts/Calendars>On).
As far as troubleshooting your iCloud backup, first try turning off iCloud backup in Settings>iCloud>Storage & Backup, then delete the backup from iCloud by going to Settings>iCloud>Storage & Backup>Manage Storage and swiping over the backup and tapping Delete, then turn iCloud backup back on and try backing up again.
If it still won't back up 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 the backup is successful, then the camera roll and/or one of your apps is interfering with 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 offending app and exclude it from your backup.
