Update on my situation (your results may vary). After consulting with Microsoft and Iolo tech support, I now know that I am missing vital registry keys. Apparently this is a known issue with Iolo System Mechanic 12.5 for which there is currently no fix. I did not have a restore point old enough to roll back the damage. Therefore, the only solution for me is a tedious refresh of my system. Because I started with Windows 8.0 and upgraded to Windows 8.1, I had to pay $15 to get a refresh disk for Windows 8.1 from Microsoft.
Both Microsoft and Iolo assure me that once I refresh my system, indexing will work again - and I will have to reinstall all of my software. I think I will leave off Iolo System Mechanic for now.