If I download a new Windows 10 from MS and run the media creation gizmo, will it install 1607 over my defective 1511 install?
Download the Media Creation Tool. Read the instructions on burning DVD or USB.
Do a Custom install. Pick your Structure (C:) and then click Format. Put Off until it does the format then install.
Do not enter any key. Just click on the note at the bottom, the Bounce, Do this later, or I do not have one.
This is called a clean install.
Before you try backup your data. Also make a copy of the Download Folder if you have not cleaned it out.
You can copy the download file to your new Download folder and reinstall your programs without having to search the Internet.