Well, you seem to have an older system which makes it a little harder to find drivers for it. If you know who made the network adapter on your system you might be able to find drivers from Fijitsu, or the adapter maker or even a third party. You should also realize x64 bit drivers for that time period were far less available than they are for the newer equipment. In some cases you can use a Vista driver for the equipment, and even an XP one possibly in compatibility mode.
I would look for drivers in both 32 bit and 64 bit versions. If 32 bit versions are more available, I would think about changing over the Win 7 32 bit for better compatibility. I did not see your model on the Fijitsu site, but you might look in the download section for drivers for network and audio to see if any type of driver is available. Win 7 contains drivers for many types of equipment, but from what you seem to be saying, those are not working, so you need to find what you can elsewhere.