Safe mode never completed. Another broken application alongside Time Machine. I let it run for about 8 hrs. Yet the drive testing tested just fine.
I reloaded the OS. No effect on the problem.
I never found any reason for Time Machine to not work.
You guys are as clueless as I am.
And this reporting tool didn't give a single clue why Time Machine is not working. In fact it said Time Machine is not configured which is actually untrue and there is no reason to believe it is unconfigured. It's not helping this reporting app just talks trash and has no serious facts behind it's conclusions. It's only gripe is my hard drive is old and thinks my hardware is obsolete. No doubt an excuse for software failures.
I appreciate your help though.
I've taken all your advice and I will be installing a new drive next week. I did all the cleanup and it didn't matter.
I did get the backup software Acronis to work. It took 5hr 20mins to complete the first backup. The incrementals are taking less than an hour. The backup is only 329GB. Certainly nothing Time Machine should not be able to handle. Maybe Time Machine should get some error messages into their software when it doesn't work. Help customers out for a change instead of cover up issues.
So I have a backup now at least.
I will let you know if I find anything after I replace the drive.
I'm not going to let this system become a boat anchor like my iMac when Apple decided to stop supporting it 6 years after I bought it.