!! Update 05 Aug !! - READ HERE FIRST
It seems that CD versions of SC4 will not run under Windows 10 - The necessary OS support files for validating SafeDisc2 copy protection simply isn't part of Windows 10. This issue is not unique to SC4 either, SafeDisc and associated technologies were widely used by game discs for such validation.
For now, unless MS decide to retroactively support it, your only option appears to be a digital version of the game which will not have such copy protection. If you put your CD-Key into Origin they will provide you with a free digital copy of the game, so it needn’t cost you any money to resolve.
This thread is aimed at users who cannot run SC4 using Windows 10, if your games starts but has other issues, this is not the place to go into that. The only way to try and understand why certain users can not get the game to work, and hopefully, find a solution, is to start gathering some data.
-Note-
I've removed the superfluous information from this thread, to avoid confusion. But in-short the summary above explains the issue here.