Right-click Network 'hood, My Network, or whatever it is in your OS. Now you'll see an icon for your LAN connection. Right-click that in and choose properties. At the bottom of the "general" tab should be a check box labelled "show icon on taskbar". Clear this check box.
This is on Win2k. It may be different for 9x/ME. If you can't get it, holler and I'll look at home on my 98 box.
Oh... if this isn't the problem... it's drivers. I never liked 21.83, it was a nasty build. Try the latest WHQL build since this version isn't working.