so when I click play in fallout 3 GOTY it doesn't run, instead, it just doesn't run and reset itself.

"Launch Fallout 3" shortcut runs "FalloutLauncher.exe"

Try playing from the Fallout3.exe (don't run it from the Launcher). You have to navigate to the folder where the game and launcher is, then click Fallout3.exe . I think the Launcher is glitchy...

The launcher for Fallout 3 has been known to be glitchy, it certainly has been on every version of the game I have owned for PC including the official physical release of the game.

EDIT: The GOG version has worked spectacurlarly and I have had no issues with the launcher.