I've been doing a bit of research in the question. For some users, there seems to be a problem with the SafeDisc copy-protection software which prevents them from running the game unless they right-click on the game icon and select "run as administrator".
https://answers.microsoft.com/en-us...ndows-10/8a86d2a9-9118-4b3a-a66f-6d409da3e517
It's reported that installing the v3.19 patch will fix the issue, but it might be necessary to have the "Beyond the Sword" expansion (which I do have as part of the Civ IV Complete Edition). The v3.19 patch is available here (and likely other sites as well, the link is to a German site):
http://civilized.de/www/content/index.php?cat=civ4_downloads
Of course, as I read further into the Microsoft Answers thread, it appears that the "Complete Edition" doesn't have the above problem, only the original PC-DVD release with the separate expansions. And the most recent post says that if you contact 2K Games and provide proof of your ownership of the PC-DVD (probably by providing them with the valid product key on the original DVD), they'll give you a key to get the Steam edition at no extra cost:
https://steamcommunity.com/app/3900/discussions/0/521643320354942961/
EDIT: I just sent 2K Games Support a message to ask them what proof of ownership they require. I didn't find a product key in the DVD box, so I took photos of the disc and box (with the price sticker still on it from when I bought it at Best Buy years back) to prove I legitimately own the disc version.
EDIT EDIT: Success! 2K games replied, asking me to send them a photo of the game case and disc accompanied by a handwritten slip of paper with the support ticket number on it. I took the requested photo with my iPhone and emailed it to them before I left for work today, and a few minutes ago they sent me the Steam product key. I wonder if this would work with other manufacturers for other older games I own that are on Steam for which I still have the disc/box?