I have exactly the same graphics card so had the exact same problem, but i found a very simple fix online and managed to get it working only today! Go to http://www.oldblivion.com/sm/index.php?topic=6928.0 which will provide you with a link to download the necessary file. There will be a few things in the zip file and the instructions tell you to modify your drivers, i didn't bother- it wasn't necessary for me. Copy the d3d9.dll file from this into your fallout goty folder, which you can find by going into your computer, finding steam, opening steamapps, then common and then fallout 3 goty and just drop it there.
Thats all i needed to do! - though i highly recommend that if you choose to do this you set all settings to LOW.
This may not work for you, and if so you are probably going to need a new graphics card if you want to play it, but hopefully it does
NOTE: This works by bypassing some protocol that stops the game from running if it doesn't believe you have the graphics card to support it by telling the launcher that you have an NVIDIA GeForce 7900 GS- which you don't. Doing so will put added stress on your system which is of course never a good thing. It is obviously better to consider buying a new graphics card rather than forcing your computer past the safeguards!