No Sound Windows 7

Unfortunately, being a slightly older S478 motherboard, Asus only has XP drivers available for it, no Vista or W7.
Can you check in device manager to see if it's recognised under Sound, video and game controllers? If it's not in there, it may be an unknown device.
Right click it - properties - Details tab - Hardware ID, then copy and paste the two results back here

The onboard chip that you have is an AD1980 6 channel Soundmax, which unfortunately, Asus stopped using quite a while ago (prior to Vista). The only available Asus drivers are for XP. Someone please correct me if I'm wrong here, but I don't believe that XP drivers work at all with W7.
There is, however, A Vista driver available for a Dell motherboard that has the same chip. Uninstall your current (not working) driver first, then right click the installer setup - properties - set compatibility to Windows Vista. Run the setup and post back to let us know how it goes :)
Drivers and Downloads

It won't let me download the file it would only let me install it, then after trying to install an error message reads: Application cannot be started. Contact the application vendor. Can I install a PCI sound card, and if I can could you make a recommendation as to which make would suit my mother board, and do I need to go into the Bios and disable the OnboardAC97 Audio Controller before installing the Sound Card?

I went back and download the driver to my hard drive followed your instructions and I got an error message: this application does not support your hardware.

Sorry about the hiccup with the Dell driver download manager... I didn't realise it wasn't a direct link. If you didn't get the file before, you can download it from here: http://ftp.dell.com/audio/R145551.EXE

There are 2 ways to get it to install the drivers for your sound chip:
1. Right click the R145551.EXE file - properties - compatibility tab - select Vista
2. Use a program like Winrar or 7Zip to extract the files from R145551.EXE
Click Start - right click computer - properties - device manager - expand Sound, Video and Game Controllers - right click SoundMAX Integrated Digital Audio - update driver software - Browse my computer to where you extracted the files.
--The 2nd way will give you a cleaner installation.

Your motherboard has 3 PCI slots on it, as long as they're not all occupied you can fit in a sound card. What I would recommend to you would depend entirely on what you do with your pc, what speakers you use, how much you value audio quality and how much you want to spend.

This is the version.txt file included with the installation:
Title: Audio: Analog Devices ADI 198x Integrated Audio Driver
Version : A25
OEM name : Analog Devices
OEM Version: 5.12.01.7010
Computers : Dimension: 2400, 3000, DE051; OptiPlex: 170L, 170L, GX270 / GX270N, GX280, GX520, GX620, SX270 / SX270N, SX280; Precision: 360 / 360N, 370, 450, 470, 650, 670
OSes : Windows Vista 32-bit Business,Windows Vista 32-bit Home Basic,Windows Vista 32-bit Home Premium,Windows Vista 32-bit Ultimate
Languages : Brazilian Portuguese, Chinese-S, Chinese-T, English, French, German, Japanese, Korean, Spanish
Created : Tuesday, November 06, 2007

I followed #2 of your direction above but was not successful. Error message reads: "The audio Driver Files do not support your computer Hardware". I would like to go ahead and spend about $40.00 for a Sound Card. It is my wife's computer so the sound card don't have to be special. She only plays CDs. So please give me your recommendations and procedure for installation of a Sound Card that will work on Windows 7. Please tell me if I need to disable the Onboard AC97 Audio Controller in the Bios before installing the Sound Card?

Creative Sound Blaster Audigy SE 7.1 Channels PCI Interface Sound Card - Retail

Sells for around $25 on newegg.com. There are Windows 7 drivers available on the creative website. Please check if/when you get it that it's an audigy se, as there is also an audigy 2 se which will need a diferent set of drivers.
To install:
Turn the computer off and remove the power cord from the back of the case.
Remove the retaining screws for the side panel (on a tower case, usually the left side) or the top panel on a desktop.
Remove all other cables at the back of the case if it's necessary as you may need room for the next step
Lay the tower case down on it's side with the feet facing you.
Either use an anti static strap, or ground yourself by touching a metal part of the case chassis.
Locate the white PCI slots, you'll have 3 in the bottom left section of the motherboard. Choose one that lines up with one of the expansion card slots at the back of the case.
If necessary, remove the metal strip or retaining bracket that is blocking the expansion slot which lines up with the PCI slot that you're going to use. These are often held in with a phillips head screw.
Remove the sound card from it's anti static bag, holding it by the bracket and/or the edge of the card.
Position it just above the PCI slot, making sure that it lines up with the PCI and expansion card slots.
If it all looks ok, gently push it all the way into the PCI slot, then screw it into the case using the phillips head screw from the expansion card blanking strip/bracket.
Follow the directions on the installation guide or manual supplied with the sound card to install any additional cables, if necessary. Refer to the motherboard manual to connect the other ends of the cables to you motherboard. There may be a thin (about 2 - 3mm wide) cable that goes from your CD/DVD drive to the motherboard, disconnect the motherboard end, and attach it to your sound card where it says either CD or Aux in, the sound card instructions will tell you where to put it.
If you don't have the motherboard manual, click here, on the left side of the page, under P4SGX-MX Related Link, click download - select XP - Manuals - Version E1242 - Global (not DLM).
Plug it in, turn it on, enter setup - usually by pressing delete, F2 or F10 during startup. Refer to your motherboard manual on how to disable onboard audio in the bios section. Exit bios, yes to save settings.
Your system will reboot, you can then install drivers if W7 doesn't do it automatically, play something, put the side/top panel back on if it's all ok.

Alternatively, you could just plug in a USB sound card, I haven't used one before, but I don't like the idea of them... just another thing hanging outside of the box :P