I got it to work though! So if you are experiencing this problem as well this will be a tutorial on how to fix it!
First of all I'm running Windows XP SP3, so this might only be the solution to people with this problem on this OS.
1. Locate the directory of GFWL: C:\Program Files\Microsoft Games for Windows - LIVE\Client
2. Open either GFWLive.exe or GFLWClient.exe
3. If it opens successfully, that means I have no idea what your problem is. It shouldn't open and instead give you an error box saying that you need Windows Live Sign-in Assistant. Click OK.
4. Download Windows Live Sign-in Assistant and then install it.
5. If it installs then success! However, for me it never installed but rather the installation ended prematurely. I had no idea what the problem was. As I was looking around for the solution to this problem I came across a Windows Update fix. Last year my computer got a virus and windows update was turned off.
This icon would always appear on the taskbar next to the other icons. Even when I turned automatic updates on through the control menu, It still wouldn't actually turn on.
It would always show the Automatic Updates in the Windows Security Center as it was Off. Right now I have it on as I got it fixed.
To do this go to this website and follow the instructions (clicky).
6. Once you have inputed the follow command into the run prompt. It should say that it has been resolved.
7. Automatic Updates should now be on and working! Now try installing Windows Live Sign-in Assistant again. This time it should complete and work.
8. Now Games for Windows - Live marketplace should work and open when you open it. And it should know appear in game!
Hope this works for anyone with the problem running on Windows XP SP3. This is just one of the solutions. The one that worked for me! Enjoy!