I've tried downloading the PhysXDownloader.dll, nvd3dum.dll, and redownloading the GeForce 8600 GT drivers, but I'm still getting this error message.

1 - Never download individual DLL files. Always identify what package the missing file belongs to and download a proper installer from the official source.

2 - Sacred 2 (and some other games from that time period) requires the PhysX legacy drivers.

Thanks for that, I downloaded the legacy drivers, and now it's saying that PhysXLoader.dll is missing. Again.

Hmm. I found a copy of PhysXLoader.dll from an NVIDIA Corporation folder elsewhere in the computer and copied it to the System32 folder, and tried again. Almost the same error from the OP came up, except this time it's saying [\\.\DISPLAY1] instead of [\\.\DISPLAY10].

That is exactly the kind of thing you should not be doing. By now you most likely have multiple incompatible versions of files scattered around. You need to clear out all the files you manually copied around, and then reinstall the drivers properly (both the latest ones and the legacy drivers).

Well I did that, and now the message is about DISPLAY4.

In the game's install folder check for a folder called "__redist" there may be required redistributables in there.
Like PhysX-9.12.1031-Legacy, and PhysX-9.13.1220 Just keep in mind that some games may want a different version of the file potentially causing compatibility issues if put there. So generally unless you're certain you want the file in System32/SysWOW64 you could instead put it in the same folder as the executable for the game, (though with this it is sometimes located in GamePath\PhysXLocal\PhysXLoader.dll). Programs have a habit of checking for such things in certain places in a certain order, the path the executable is run from is one of the first places it will check.

So having said that, if reinstalling the redistributables doesn't help, it might be worth searching your computer for any other versions of the .dll in question and seeing if you have different versions and try putting different ones into the games folder to see if one works for you. I'm not sure I'd get my hopes up in this case, best bet is probably to uninstall all PhysX/nvidia stuff and reinstall.

I had this and other similar errors with this game until yet. I tried many PhysX versions, compatibility, run as admin and so on, nothing helped.

1, I deinstalled the game
2. Deinstalled all physX installations
3. Redownloaded it
4. I turned off firewall and AV
5. Closed almost any software
6. Tried to install it, at the end i got an error about missing files, but the setup still finished and I got again the same error while running the game.
7. Tried to install it with integrity check on again and got an integrity error.
8. Redownloaded the broken file.
9. Installed it again without errors yet.
10. Installed the bundled physX software
11. Hoped.
12. Started the game and it work.

Afterwards I tried to install a newer PhysX legacy driver and started to get the same error as you do, so you have to use an older PhysX legacy driver (which is bundled with the game, see the __redist folder).

Also it might fail while using Gog Galaxy.

Uninstall all physX from your pc.

Run CCleaner on your registry and clean it.

Install the PhysX package included in the redistributibles folder.

Don't forget to run as admin!

Profit.

NOTE: Depending on your particular setup, you may have to set the game to run in compatibility mode for Vista or even XP.