I had the same issue - Launcher starts, you click "Play Distant Worlds", then nothing happens. No error message. Just nothing. Since I hadn't played DW on my current PC, this was the first time I'd tried it in at least a year, maybe two.
First give this a read:
Some basic things to try, but it's a little out of date as it hasn't been updated in 7(!) years. None of it applied to me, but it's worth a try.
My issue seemed to be Windows Media Player that's been removed from Windows 10 in one of their recent "updates". Microsoft have also altered the method to restore it, so google will generally tell you the old method to restore it, which doesn't work. Never download it from a 3rd party, that's just asking for trouble.
So here's what I did to get it working on my system:
1. Make sure your DirectX drivers are up to date. Go to:
The web-based DirectX installer should automactically download. Run it. If you're missing anything it should install.
I wasn't, but I also play a lot of older games on my potato PC, so have most stuff older games require anyway.
2. (Re)Install Windows Media Player (WMP). Follow Microsoft's instructions here:
That's it. Got DW running at least. If it crashes after this, you should at least have more to go on than "nothing" which a missing WMP gives you.
You can automatically skip the opening movie by editing the startup.ini file as described here:
Some say that fixed their problem with the game not starting, but it didn't work for me by itself. Just reinstall WMP as above, at least you can watch the intro that way and skip it in future.