David,
The first two having a null ModuleDefID and null ControlKey are the ones causing the error when trying Host Settings. However, the root of the problem is a bit more complicated than can be fixed by adding a control key value.
Back in the 5.x version line, many of the admin and host modules formerly located in child folders of the /Admin folder were relocated to child folders of /DesktopModules/Admin and their registration in the ModuleDefinitions, ModuleControls, and other core tables adjusted accordingly. Apparently during some earlier upgrade this reorganization failed to occur leaving some serious data integrity errors in the core tables.
In the cases of the Feed Explorer module, a clean install of DNN 6.1.4 yields the following in the ModuleControls table
| ModuleDefID |
ControlKey |
ControlSrc |
| 93 |
Null |
DesktopModules/Admin/FeedExplorer/FeedExplorer.ascx |
There is no entry in ModuleControls for any AdSense.ascx control related to the Vendors module. It is also quite possible that other module defintions and module control registrations did not get upgraded properly. Please check to see if you have an entry in the ModuleControls table for the correct ControlSrc above with a non-null ModuleDefID. If you do then you should be able to delete the incorrect row for FeedExplorer.ascx having both the Null ModuleDefID and Null ControlKey so that Host Settings page can be opened.
By running some queries on the Packages, DesktopModules, ModuleDefinitions and ModuleControls tables we can probably work this out but unfortunately I don't have time to look into it further tonight.