Welcome to the forums KenNC.
I know how I would try to remove a constant noise from an audio stream within a dvd, but it is not a simple process. I can outline it if you wish. By the way, do you have a menu on this dvd that you want saved? If so, the process will be a bit different.
It would help to know the format of the audio stream. DVDs in the US use three different types of audio, normally AC3, but LPCM and DTS are possible. (DTS is virtually never used by amateurs).
You'll need to demux the audio and video streams from the dvd-video. You can use PGCDemux for this: http://www.videohelp.com/tools/PgcDemux Make certain to save both the audio and video streams (put a check mark in the box to save the video also).
The tool I would use to adjust the sound is Audacity, a free audio editing program. You can find it here: http://audacity.sourceforge.net/
Get the 1.3.12 beta, and get the ffmpeg and lame libraries as well. http://lame.buanzo.com.ar/
By using the ffmpeg library in Audacity, you should be able to import an AC3 audio stream. LPCM would go straight in without problems, but sometimes even using the ffmpeg library, you have issues importing AC3 into Audacity. If you do, then you'll have to uncompress the audio stream to .wav.
One tool for uncompressing AC3 to .wav is called HeadAC3he: http://www.videohelp.com/tools/HeadAC3he Very simple to use.
Still with me? At this point you'll want to import the AC3 or .wav file into Audacity and follow this guide for removing noise from your audio stream: http://wiki.audacityteam.org/index.php?title=Noise_Removal
Once you have removed the noise, click on File-->Export and save as an AC3 file. It will need to be 48khz to be dvd compliant and no more than 448kbps.
Now its time to rebuild the dvd-video. For this, you'll need an authoring program, the video stream you saved earlier and this new ac3 file you just made. There are some simple authoring programs available, but you won't be able to make very snazzy menus with them. You may already have an authoring program, since you made a dvd from a video earlier, but here is a free one that will accept these demuxed streams: http://www.videohelp.com/tools/DVDAuthorgui