Restore database failed - is incorrectly formed and can not be read.

I use restore database to create TEST and DEV copies of my backend to work on. I was restoring a backup as a new TEST database. I noticed that the restored version did not have a newly created table trigger put in the PRODUCTION. So, I backed up the PRODUCTION database again, dropped the TEST database again, and restored TEST from the backup of PRODUCTION just created. Still, it did not contain that table trigger.

I did this a few more times. Still the triggers weren't showing up in the restores. So I backed up again, except this time I selected "Overwrite all existing backup sets" in Media Options. Then tried to restore. I am now getting this error. I've tried to backup again, and still every backup now will not restore and gives me this:

Msg 3287, Level 16, State 1, Line 13
The file ID 10 on device 'C:\Program Files\Microsoft SQL Server\MSSQL11.MSSQLSERVER\MSSQL\Backup\VeteransNewsNetwork.bak' is incorrectly formed and can not be read.
Msg 3013, Level 16, State 1, Line 13
RESTORE DATABASE is terminating abnormally.


I deleted all backups from the actual folder and tried again. Still same thing. Why are all backups incorrectly formed now and cannot be read? How can I start to fix this?

Thanks for the advice!