Not sure if you're still having the problem, but I have the exact same laptop and solved it with a vista audio driver.
Click on the link below or go on alienware.com's support > knowledge base, and search for '6051' which will bring up just the answer for case 6051, it will have various drivers, at the top is W7 64-Bit, but if you're on 32-Bit then that won't work. The driver that worked for me was the Vista audio driver, just scroll down to where it shows:
Windows Vista
- Audio driver
And that's the driver that got my m9700 running perfectly. Audibly at least. If you have problems still, try uninstalling any drivers you currently have for audio/media and try installing this again.
If you still have problems, maybe try reformatting and then having this driver be your first priority.
If you STILL have problems, mess about with anything else you can think of, including the physical volume wheel on the side of the laptop........... and if all else fails, then your sound device might be broken.
A good thing to note is that I didn't use the wizard to install the audio driver, I used the 'install.bat' file. Brings up a Command window which installs the driver in the background. Do nothing until it's finished.
The installer comes in a zipped file, I used WinRAR to extract all the content. You can get a trial version for free by googling it.
Hope you get it working. :3
- Roa