I launch it, a black terminal appears with some log text, then the black window with a white square in the middle appears, then it turns all black and that's it. I can see the cursor, move it around, and I hear a sort of ambient music, but there's nothing to click.

I already tried the compatibility mode and running it as administrator at 640x480 as well as making sure to install the .NET and XNA redistributables.

I'm on Windows 10 1607.

EDIT #1: The GUI is black
Clicking around the black screen the game closed. I opened it again and clicked exactly where I clicked before and the game exited again. That's the exit button. Some more clicking later the sound increased in volume, and then decreased, I kind of found the volume slider through the dark. I'm in the sound settings! So it seems the game is there, it's just the GUI is black.

After trying many things suggested all over the interwebz I finally got it to work. I downloaded the settings file from the game's website and pasted it in the game installation folder. Overwrite if there is one already there.

hacknet-os.com/Support/Settings.txt

Time to use my mad "l33t 5k1llz".