Here is another idea...
You have two variables in your failure equation.
The first is Windows backup itself and the second is your new 1TB external drive.
You can eliminate the first variable by making a simple backup of something small (just one folder) and backing it up to your local HDD that you know works fine.
If that works, you can be reasonably confident that the problem is not with Windows itself. You also might see if you can restore that simple backup to be sure the entire process works from end to end.
If that same backup fails when you attempt to put the backup on your external drive you will have narrowed down where to start looking for the problem.