Hi,

First of all, start Backup Service under administrator account: go to Tools > Change Service Account, enter local administrator account name and password, click OK.

If that doesn't help, then using backup operators options should solve the issue, unless the files are encrypted.
Members of the Backup Operators group can back up and restore files and folders regardless of ownership, permissions, or auditing settings. To do this, you need to:

1) Open Computer Management
2) In the console tree, click Groups. You can find it in Computer Management -> Local Users and Groups -> Groups
3) In the details pane double-click Backup Operators.
4) On the Backup Operators Properties dialog box, click Add.
5) On the Select Users or Groups dialog box, next to Name, type the domain and user name of the person you want to make a backup operator Type the domain name first, then a backslash, then the user name. For example,\\Domain\User.
6) Click Add, and then click OK.

Note:
-You must be a member of the Administrators group to designate users as Backup Operators.
-To open Computer Management, click Start, and then click Control Panel. Click Performance and Maintenance, click Administrative Tools, and then double-click Computer Management.

After that edit the backup plan and check "Backup Operators" option on the Advanced Options step.

If all of the above steps don't help I suggest to send us the diagnostic logs via tools > diagnostic menu.