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First off, while you may not like the one rulebook, some fans did an "update" to bring it up to speed with Fallout 3 and some of New Vegas. These rules are a bit cleaned, but still a bit frustrating. You can find them (and other tabletop variants) here:
http://www.nma-fallout.com/forum/dload.php?action=category&cat_id=63
Second, I will second using Alternity. It may be a bit clunky for some, but it will work and there's plenty of settings that will work. As any game, the mechanics may interfere with the feel of the setting, though.
Third, SPECIAL was based on a variant of GURPS. That being said, I'm not a GURPS fan, and wouldn't use it.
Fourth, have you taken a look at Deadlands: Hell on Earth? The setting is similar, only with magic-like things tossed in. The original version of the rules, with deadly combat and location-based wounds, fits in perfectly with what we see in the newer Fallout games. Otherwise, take a look at the new Hell On Earth Reloaded using the Savage Worlds settings.
Fifth, there's a collection of RIFTS settings that could work to get you started, "After The Bomb" being one of them. I'm not too bit on RIFTS, but some people just never can get enough of it.
Sixth, World of Darkness (old and new) may be versatile, but I don't think it has enough grit to be a Fallout game. Some useful mechanics, but overall doesn't really capture the feel of it.
Finally, you can easily tweak most generic systems to make characters within a setting, but the mechanics may impact the actual FEEL of the game. The various d6 series (d6 Space and d6 Adventures, primarily), Savage Worlds, Cortex (either Battlestar Galactica or the new Marvel, depending on preference), Tri-Stat, FATE, PDQ, etc.
tl;dr: you can take ANY game you like the mechanics of, tweak the setting, and you're done. I just made suggestions from experience.