What Engerek01 said. Try waiting. For a looooooong time. I don't know Windows 10, but this happened on my Windows 7 desktop PC once when I tried to install a GOG game. I double clicked the installer and nothing happened. I thought it didn't recognize my double click (happens sometimes, when you move the cursor and drag the icon slightly), so I double clicked the installer again. And again: Nothing happened.
I didn't go to the task manager, but started to Google for possible problems. After a couple of minutes I got an UAC prompt (the "Do you want to allow the following program..." pop up)... It was the one from the installer. I hit yes, started the installation, went to the task manager and found another UAC process there, completely idle, waiting for nice weather or something -.- It took anotther minute or two before it became active again and gave me the pop up.
Again, I don't know Windows 10, but this is something that can happen on Windows 7 sometimes.