Check to see that you have all the updates from MS for ME, and check with the maker of your NIC to see if they have any driver upgrades.
Check the LEDs on the hub/switch. Do a file download from the Internet, then download a file from one of the other machines on the LAN. If it's a hub, there'll be "collision" LED, if that's lit up alot, chances are someone (like the box you're downloading from)has full duplex selected, which is a bad thing when connected to most hubs.
If you really have a switch, then check the other LAN computer's NIC settings. It may not be playing well with the "autoconfigure" feature on the switch for speed & duplex. Manually set the speed & duplex to 10 half, then try a download. If that works, take it to 100/half, if that works, try 100 full. After you've changed the speed & duplex settings, disconnect the computer from the hub/switch for a bit, then plug it back in.
Good Luck
Scott