I have had a problem with this computer keeping a stable network connection for some time and have just noticed that in the Local Area Connection Status screen that the sent packets reset to zero every few seconds. It is running win 2000 pro with an integrated nic on mb.
The first thing to do in cases like this would be to spyware/adware/virus scan the heck out of your system. Give your computer a round of spybot and adaware. If you dont have an antivirus program (or an updated one) load up Avast. It is free and does a damned good job.
Do you notice the cable disconnected message pop up at all? or the little symbol in the system tray showing two monitors with a red X next to them?
Do you have a home router?
Are you wired or wirelessly connected to it?