OK, I managed to edit an AVI here, with VirtualDub and Audacity.
For source material, I recorded an AVI with my WinTV card. Then used
that for a quick test.
VirtualDub allows the sound to be separated from the video.
Then, you take the sound into Audacity. You can use "amplify" in there,
then select "Normalize" and set it to -10dB. The program finds the loudest
section of the audio, sets that to -10dB, and everything else is scaled
down in proportion.
Once the audio is processed, you select "Export" from the Audacity file
menu, and export as an audio file.
Then, back in VirtualDub, you ask VirtualDub to "Audio : Audio From Other File"
and point VirtualDub at the new sound track. When VirtualDub is used to
save the new video ("Save as AVI"), now you have a processed audio track.
This is not a NLE as such, as you are processing a whole clip in one
shot, extracting audio and adding it back in, in a couple runs.
A weakness with AVI, is the file format itself. There is a standard for
AVI files larger than 2GB, but I have had a few problems with it. As long
as your clips are short ones, then you might not run into any of those