Well, I finally got Opera working properly again. Here's what I did:
Ran a malware scan; no problems found.
Made a backup of all my Opera bookmarks, settings, etc.
Uninstalled Opera and told it to remove all Opera-related data.
Ran several registry scans, using Registry Mechanic and ccleaner, until all remaining traces of Opera were removed.
Reinstalled Opera, this time to folder C:\Program Files\opera1217.
Now it works and I can access www.deseretnews.com once again.