On my previous laptop I could right click on the DOI and it would transfer it to my zotero library. Now, it not only does not do that, but it will not communicate with Word.
Do you have the Zotero Connector extension installed in your web browser? You can download it from here: https://www.zotero.org/download/
As for Word, check if you have the Zotero add-in installed by navigating (in Zotero) to edit -> settings -> cite and scrolling to the bottom of the menu. If it says the add-in is installed, try reinstalling it and restarting Word.
@JoleenRichins: I think you're misremembering something. You don't right-click on a DOI anywhere to save it to your Zotero library. See Adding Items to Zotero to make sure you're clear on all the ways to add things to your library.
Upgrade Storage
As for Word, check if you have the Zotero add-in installed by navigating (in Zotero) to
edit -> settings -> citeand scrolling to the bottom of the menu. If it says the add-in is installed, try reinstalling it and restarting Word.