"No proofing" is a "language" (as far as Word is concerned) that is not checked against any dictionary. It's an attribute of the text in the document (just as, for example, bold would be an attribute of the text), which is why reinstalling Office or trashing preferences doesn't solve your problem.

The procedure described allows you to find a text that is designated "No proofing", but it doesn't tell you how to change it.

Assuming you are writing in a single language: select the entire document (Select All from the Edit menu). Then pick "Language" from the Tools menu. Select the language you are writing in (for example, "English (U.S.)"). Then click OK.

There is more than one "Add" button associated with the Word spelling and grammar checking.

When you select "Spelling and grammar..." from the Tools menu, a dialog labeled "Spelling and Grammar: (language)" opens. The add button on that dialog is used to add a word to the currently selected custom dictionary. It is greyed out, that implies the current custom dictionary is not selected, it is not writable, or is not of the "Language" of the text.

On that " Spelling and grammar " dialog, if you click the "Options..." button, the "Spelling Grammar" dialog opens (note the name is distinguished only by the lack of the conjunction). If you have more than one custom dictionary, the custom dictionary displayed in the "Custom dictionary:" pulldown menu is the one to which the "Add" button in the "Spelling and Grammar" dialog will add the word. (that was a mouthful)

On that "Spelling Grammar" dialog, if you click the "Dictionaries..." button, the "Custom dictionaries" dialog opens. This dialogue has an "Add..." button that is used to add a custom dictionary to the list. In this case "Add" is used to add an already-existing dictionary to your list. If you don't already have a custom dictionary, you would click "New..." instead To make a new, empty custom dictionary.

I have illustrated these three dialogs here for reference.

You might want to save a compressed version of your Microsoft Preferences folder. Word routinely trashes its preferences. This is not a big deal, but recreating what you are accustomed to wastes time -- 15 seconds versus 10 minutes.

If you do not do this, Word may not default to the dictionaries you want it to use. You can create a bazillion dictionaries, but you can use only one at a time. I create spelling exceptions dictionaries for each project.