What worked for me was to turn off MSI Afterburner/RivaTuner. These usually clash with some games.
You can turn them back on once the game is up and running as should. :)

Don't do this!

I have no idea how the GOG version of DWU works, but I've been using the original versions of DW and DWU from Matrix since they were released, on different PC's with different Win OS's, including a very new Win10 64b Home PC, and I never had any issues with AV and firewall (I'm using Norton, by the way, which isn't really liberal in letting things through).
You may or may not block the attempt to establish an outbound connection - if you don't (and GOG didn't modify the original Matrix version), you get Matrix ads and the option to update the game (and I have no idea what data about your PC are collected along the way), but I guess GOG will offer updates, if there are any, directly. The game runs fine when you block all outbound connections it tries to establish.
And I recommend to every one not to play games forcing you to disable AV, to add a program file to the AV exception list - DWU is NOT one of these games!

As I said, I ignored all that and set my firewall to Deny All. I don't think support knows what they're talking about.

I think they do know. To tell people to disable AV (and firewall settings for single player games) is standard procedure when you deal with support teams. It's not lack of awareness and knowledge, in my mind, it's lack of assuming responsibility for one's actions - or how would you call it when these guys tell people (some of which are computer-illiterates) to open the door for malware and spyware of all sorts? The main priority for support teams is achieving their performance goals, and this means closing tickets as quickly as possible and motivates to use standard prefabricated replies.
I've been playing lots of computer games for many years, and I still have to see a single game that really wouldn't install or run without disabling AV. Perhaps there are such games, but they can't have been developed by developers I can respect, and I would certainly refuse to install or run them.
PS: This is not to be confused with false AV alerts, but that's a different story ...

Coming from a thread on steam, you need i-net explorer for the ingame wiki und windows media player for...who knows what. Some sound files i guess. After installing these two the game startet for me

After trying many other things, this is what worked for me:

Open the Startup.ini in a text editor (like: Notepad) and change:
playmovie 1
to:
playmovie 0

I have the same issue. I do not have WMP installed and am unable to do so. (Unless someone can guide me to a download for an installer) I am running windows 10 pro (non n or k or w/e) with 32gb ram, gtx 1070 (with latest drivers) and a i5 6500. Everytime I click play on the launcher the launcher just pops back up and nothing happens. over and over and over. I am about to file for a refund to be honest.

Have you tried to run the exe directly (bypassing the launch screen)?

What Oxygen1234 said in the first post works well. Change the file indicated and all will work

Nope. I tried that to no avail. I also tried using the exe directly. Same thing.

Hmmm, the only issue I have ever had with it was making the movie. Sometimes users had to set it to not play and then the game started. I have it on Steam as well as through Matrix(Slitherine) games.

Did it install all the .net files and XNA as well? I know those need to be there.

Did you try disabling the intro movie? oxygen1234 gave instructions on how to do it above.

Yes as well as installing all the other things.

There is no WMP. I have been going over this with the microsoft support already. I am probably just going to have to get a refund and reformat at somepoint or just get an ssd and do the os on that.