Didn't have time to see if there was a suitable fix, but an easy enough way (I think...) to get rid of the problem is simply remove the default beep sound from windows. To do so, follow these simple steps:
1. Go to Control Panel
2. Double-click "Sounds" (if you use the non-classic view, you will have to click "Hardware & Sound" and then "Sounds")
3. Click on the "Sounds" tab
4. The first one listed under Programs is likely Windows; just a few items down is the sound "Default Beep"; select this
5. At the bottom is a drop down list that likely says "Windows Ding"; click it and scroll to the top and pick "(none)".
6. Hit OK and viola! No more dinging!
Of course, this will remove the dinging noise from the computer altogether, and not just in Fallout 3. Not a big deal, but just something to be aware of, as you can always change it later if you want. I believe there is another way to have the sound come from the speakers instead, in which muting them would solve it, but I'm not 100% sure and this way saves you from having to get rid of every sound.
If anyone else has a more specific answer to only alter it for F3, feel free to reply, but I think this will solve your problem. Good luck!