If it's happening in a new, empty document, there's a very good chance the plugin's Document Preferences window is just opening in the background behind Word. Restart Zotero and try again, and if you get the progress bar, look through the Zotero app's windows.
If you can't figure it out, provide a Debug ID for Zotero startup through reproducing the problem, using the Help → Debug Output Logging → "Restart with Logging Enabled…" option.
(We sometimes respond within seconds here, but there's no guarantee of a real-time conversation. Please be patient.)
Can you reproduce this with a new, empty file, instead of an existing document? If so, can you provide a Debug ID that shows that?
Are you seeing the "The citation style […] could not be found" error each time you try this after restarting Word? If that's part of the problem, we'd want to see a Debug ID that covered that happening.
After providing that, go to the app settings → Cite and make sure "Elsevier (author-date/Harvard, with titles)" is installed. The existing document you're using is likely set to use that, and for some reason Zotero can't automatically install it. If that style isn't installed, click "Get Additional Styles…" and install it, and then try again.
https://s3.amazonaws.com/zotero.org/images/forums/u15183051/awj7ny8dzliwa91wyey8.png
If you can't figure it out, provide a Debug ID for Zotero startup through reproducing the problem, using the Help → Debug Output Logging → "Restart with Logging Enabled…" option.
https://s3.amazonaws.com/zotero.org/images/forums/u15183051/tcxy099upeiecarv2we5.png
https://s3.amazonaws.com/zotero.org/images/forums/u15183051/a5edrju49uaj88tlqpzy.png
Can you reproduce this with a new, empty file, instead of an existing document? If so, can you provide a Debug ID that shows that?
Are you seeing the "The citation style […] could not be found" error each time you try this after restarting Word? If that's part of the problem, we'd want to see a Debug ID that covered that happening.
After providing that, go to the app settings → Cite and make sure "Elsevier (author-date/Harvard, with titles)" is installed. The existing document you're using is likely set to use that, and for some reason Zotero can't automatically install it. If that style isn't installed, click "Get Additional Styles…" and install it, and then try again.