Sharepoint 2013 Backup Failure - BDC Service

What happens when you attempt the backup through Central Administration?

I just ran a manual full backup from CA, and I get the exact same error.

What do the spbackup.log or sprestore.log files located in the backup directory say?

As I mentioned in my first post, they say this.

FatalError: Backup failed for Object BDC_Service_DB_5ed98832-97a8-439c-892d-5814f802c7bb failed in event OnBackup. For m
ore information, see the spbackup.log or sprestore.log file located in the backup directory.

Can you look here to see if there is a lock on the site?

http://sharepointyankee.com/2011/02/21/sharepoint-site-collection-backup-failedsite-left-locked/

I checked out the link.  None of my sites are locked.  I toggled the read-only switch and it didn't make any difference.  I also checked SQL to make sure all of my databases were "Normal".  They are.  For the record, my users can successfully read and write content to all site collections in the farm.  I just can't back it up.  The account I'm running the backup as is the admin/owner account and is a dbowner for all databases in SQL.

well it looks like it is failing on the BDC service application so that would not be one that users have access to, but if all the DB's look ok, then I guess thats all you can do.
I suppose if I were in your situation, I would just take a SQL DB backup at this point

So, if I have a good full backup of all SQL databases, is there any reason to mess with a Sharepoint Backup?  I've never quite understood the relationship between the two backup methods (SQL and SP).  I need to back up all content and configuration data.  If I was to need to restore to a point in time (let's say the server completely crashed), how would I go about doing so?

It would depend on your configuration.
Our own DR process that I just rewrote for our highly customized external facing web app involves a reinstall of OS, SharePoint, followed by installing our custom solutions, configuration changes, web.config changes and finally by attaching the content databases (which contain all the content).
We do not backup any configuration, or service application databases (with one exception - we do take backups of the Managed Metadata DB)

I believe MS recommends NOT backing up the configuration DB - attempting to attach to an existing config DB with new machines can cause a lot more trouble than its worth

I don't have any "custom" solutions in place that I would need to plan for in a DR scenario.  I just have a single standalone SP frontend and a single SQL backend.  Do you any recommendations for articles that would walk me through the best way to recover my farm?  I had honestly never heard of MS recommending to not backup the config database.