Recently I wanted to play through Life Stories again and installed it on my new laptop - it's Asus ROG GL553 with Windows 10. The game installed without a problem and started up in a window. That's where the problem appears - although the program seems to be running, I can hear the game and it's interactive (I can skip the cinematic intro by clicking), the window remains white, so it's unplayable. Does anyone have an idea, how to fix it? Maybe Graphic Rules Maker for TS2?

Have you made sure to download and install ALL available Windows updates ? Please do so if you still haven't done that on your own computer. Also try running the "autorun.exe" as Administrator (right-click -> Run as Administrator).
Other than that, the error sounds familiar and reminds me of something I saw in another game. Can you try this here too ?
Control Panel -> Programs -> Programs and Features -> Turn Windows features on or off.
Unfold the folder named "Legacy Components" and see if the box named DirectPlay is ticked. If not, please tick that box manually and click on "OK". I don't remember anymore, but you may need to re-start the computer for the changes to take effect.
After that, try running the setup again. Good luck for now !

You mean Windows updates? Yea, I keep my system up to date all the time. I tried running it as administrator and in compatibility mode beforehand. I will check the other solutions as soon as I'm at home and let you know, whether it worked for me. Thanks in advance!

I recently played the Sims Castaway Stories and I couldnt get it to install, I had to go into C Drive and open the .exe file and run as an Administrator. I would try doing this for Life Stories too!