I open the game and it goes to the desktop, but I can see the game icon in my taskbar. It sits there for about 30 seconds, then goes away. I've tried launching as an admin and not as admin, same thing. Tried disabling full-screen optimization like it suggests in the support area, still no change. Could anyone assist, please?

All 3 games launch fine for me, and I have Windows 10. Which game are you talking about, specifically? Icewind Dale 1, IWD:EE, or IWD2? Which GPU is your PC using? If you are playing EE and are using an IGPU, that might be the problem, as integrated GPUs have difficulty handling the renderer that the Enhanced Edition uses. Have you tried compatibility mode? Have you tried reinstalling the game?

It's the IWD Complete version, and yes, I've deleted and reinstalled several times and tried compatibility mode using every Windows version option.

It also adds the admin shield icon to the desktop shortcut after the first time I try to launch the game, every time. Even after I uncheck the "run as admin" box, it keeps the shield icon.

I'm thinking I'm just going to switch my laptop to an earlier version of Windows, like Me.

Try enabling DirectPlay
https://softlay.net/how-to/enable-directplay-windows-10.html

Yep, one of the first things I did. Windows 10 is simply a shit operating system.

System specifications would help to diagnose the problem. Also, post a trouble ticket with Gog, because their support services are friendly and effective. :)

I had the same problem, but when I started the game thru Gog Galaxy , (presssing the play button) it worked.
Hopes it helps.

Another thing to try is to not install Gog in C:\Program (x86) .
Try install Gog in just C:\.
Mods work better to if you do.

Thanks
Humiz