I recently restored a Dell 600m, and no drivers for the wireless or ethernet were installed. So I plugged in a 3G stick, and Windows couldn't automatically find any drivers for it online, so I went to Dell.com, and found my model, but there's like 25 network drivers to choose from. Searching using the service tag doesn't come up with any network drivers. I've tried using the driver reset utility, doesn't work at all. And it did not come with a disc. I can only remember that it was an Intel PRO Set Wireless.
I've noticed with Dell's that it is usually a game of playing mix and match with the network card drivers. Chances are that it is the Intel driver, so give that a go first. It won't hurt the computer by trying out drivers, as the set up program will tell you that the device isn't there.
Call Dell, give them your Laptop's model # and ask them what network driver from the 25 listed you need, and request a CD as a safety net.
I suggest you to contact dell via chat, email or telephone, gave the service tag, express service and the name of the owner of the laptop and explain them that you need the model name of your network adapter, this request doesn't matter if the warranty of this laptop has expired. They have all this information, they also can provide you the ftp link of the driver.