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My SC4 installation doesn't run anymore since recent updates of my Win 10 laptop. Does anybody experience similar issues?

It's behaving the same way as trying to run a cd-installation on Win 10 = nothing happens at all after starting the exe. I got the Game via GOG as the CD thing was an unsolvable issue. I'm frustrated :(

Are you running the game in compatibility mode for WinXP SP3 and as administrator?

Your CD version doesn't work because it uses the SafeDisc copy protection system, and all currently supported Windows OSes have the SafeDisc driver disabled (Windows 10 even has it removed, I think).
Yes, I know about the SafeDisk issue... That's why I got the GOG version in a sale.

It run under Win 10 after installation and there was also no issue with the startupmanager... suppressed Intro, by the way.

Now, it doesn't run anyhow, anymore after the anniversary update (compatibility and administrator checked). I read about the issues with cams due to Video Codecs, so I thought it might be a codec or maybe directX issue.

That's why I'm asking if anybody else has these issues.... :)
Have you tried the SimCity 4 Launcher?
The GOG version works fine on my Windows 10. Try any compatiablity and get support from GOG if that fails.