I notice in Programs and Features, Windows features on or off, there is an "Indexing Service" which is unchecked by default. It does start an Indexing Service that can be seen in the Services Panel, but it should not be there. It is for an older version of Windows and should not normally be turned on.
There is a Search Troubleshooter you might try. Maybe if would find something that is not running correctly. I will look to see if I can find a reason your modify button would be greyed out, but it appears something is not running that should be. You may even want to open an administrative command prompt and type SFC /scannow to check your system files.
If you have made some modification to the registry or some other setting to turn the normal indexing off, you might revisit that.
Edit: If I stop the Windows Search (WSearch) service, I get an Indexing Options windows with no locations listed, the Modify button is greyed out, and it says Indexing is not running.... sounds like what you show. SearchIndexer.exe is the component that seems to be doing the work, if that helps any...