Lot of people complaining the game won't run for them. But lets talk about your Steam install.

If you don't have the basics down, it isn't going to help.

Two big things that I always do:

1. Never install steam in the "Program Files" directory. This puts your install under windows UAC control, which can cause problems, particularly when using mods.

Steam has instructions on how to move your steam install if you've already done this:
https://gtm.you1.cn/helpsteam/en/faqs/view/4BD4-4528-6B2E-8327

2. Always run Steam in administrator mode.

In Windows 10 (not sure on other versions of windows) you can right click on the Steam shortcut and select "Advanced" and there is a checkbox for "Run as Administrator" which has always worked for me as running the actual steam.exe with administrator permissions.

If you prefer you can go into your Steam install directory and find your steam.exe file and go under the properties->compatibilty tab and check the box to run as Administrator.

Doing this will give you one popup when you start Steam asking for permission to run as administrator.

Regarding Fallout specifically
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1. If you're running script extender, the .exe for scriptextender, i.e. FOSE.exe or F4SE.exe should be run as administrator as well, using the same method of properties->Compatibility-> Run as Administrator.

2. It can help to run Fallout 3 in compatibility mode for XP SP2 or SP3 depending on your OS and how old your PC is. This is also found under Compatibility by checking the box that says, "Run this program in compatibility mode for:" and then using the drop down box to select what you want. THIS NO LONGER SEEMS NECESSARY FOR THE NEWEST UPDATE. But you can try it if nothing else is working.