When you say it has no sound, do you mean that no sound comes from the speakers, or no sound comes from either the speakers or the headphones jack when you plug some in?
To answer the question of whether or not it can be fixed is, most likely, but not recommended (actually I would advise against it). If you are still able to hear sound through headphones, then the problem is probably the sound wire that runs from the bottom half to the top. It has probably broken from excessive bending (opening and closing the screen over time can wear out parts like this) or one of the solder contacts has come loose.
Like I mentioned before, this could probably be fixed by opening the DS and reconnecting/replacing the appropriate wire. I would not recommend it for a few reasons. The first is that you are likely to break even more when you open it. Second is that you would not be able to get into it unless you have the special Nintendo screw bit (yes, it is special, don't even bother looking in your tool box for one). And three, I would only recommend this if you can make very strong and small solder connections for your replacement wire.
My number one suggestion is to just use headphones. My number two suggestion is if you can't live without sound in the air (meaning sound from a speaker), then buy one of those small I-pod speakers for 30-40 US Dollars.
Like this one:
http://homepage.mac.com/flounder/.Pictures/TAB/podwave/podwave_dock.jpg&imgrefurl=http://theappleblog.com/2005/03/15/macallys-podwave-speakers-for-the-ipod/&h=277&w=289&sz=6&hl=en&start=2&sig2=OU7Ab2avc1nWReFcrU5Shw&tbnid=f1FrYQ9qJPU8rM:&tbnh=110&tbnw=115&ei=Rl3XRrqJGJ3EeI-s9RM&prev=/images%3Fq%3Dsmall%2Bipod%2Bspeakers%26gbv%3D2%26svnum%3D10%26hl%3Den%26sa%3DG
Good Luck :)
Bosnoff
August 2007