I had the same problem trying to run New Vegas on my laptop, background music but absolutely no sound effects. I tried everything: Removing ffdshow, running it in window mode, updating sound cards, setting priority to High on task manager, updating directx directsound, patches and updates etc.
The thing that worked for me (you'll need F3 installed) was copy and pasting the .bsn files from the original Fallout 3 folder into the New Vegas Folder. I didnt replace any files, I just added those that were not already there. This enabled all sound effects (footsteps, doors, speech, etc) except gunshots.
HOWEVER, there are many mods available that 'improve' and even replace NV Gun Sounds and by installing one of those, you should fix that issue and get a pretty satisfactory result.
Hope that helps at all, it's not a very 'neat' solution and am not sure why adding the extra files to an already complete game worked. But it did, and now it's alot easier to become immersed in the wasteland.