For me this was caused by a rogue codec. Over the course of time, the "person in hurry" way of solving codec problem is to install "yet-another-codec-pack". The lite version

. It's a valid approach, but since there are more ignorant "experts" than you think, most of the codec packs contain obscure codecs that are considered "superior" over those "crappy default windows stuff". The problem is (or what I think the problem is), the game developers work with the "default crappy stuff". Since everyone has it ... overridden by another codec ... oops.
For me it caused the game to crash on alt-tab and when quitting it. Not speaking of the music not-playing on the radio.
I used two utilities and I won't provide a full step-by-step description, since if you don't like to use your brain, buy a console and don't buy bethesda/obsidian games (I'm not saying you're lame, I have a XBOX360 and it's great with reliable software, F:NV isn't that software).
This is not something I figured out, I read about it somewhere either in this forum or else. So I don't want to take any credit.
1. Utility: GSpot2
Load the fallout music file, in the bottom there's an area called: "Proposed codec solution and tests", hit the MS A/V button nr.1. That should give you a string saying which codec is used (a file). Now use the second utility.
2. Utility: Installed codecs (http://www.nirsoft.net/utils/installed_codec.html) (if posting links is illegal, feel free to delete it, but give a thought to the following statement "is my action helpful, or am I a rule loving drone?")
Search for your file found by GSpot. If it shows something non-default (i.e. it doesn't look like MS stuff), disable it.
I had to do it twice (you disable one svcker and another takes over). Finally I was using something that wasn't on the list. Probably the generic stuff doesn't show up (?). Anyway, it was saying it belonged to DirectX and it works fine now.
Done on win 7.
(BTW, if someone tells you to reinstall your windows, just stop listening (or reading

. There's no reason, unless it's a hardware failure or you ran out of disk space (bad planning on a system partition

), everything else can be solved by the UTFG method)