Networking set-up problem Dimension 4600w/Windows XP

I am new to this forum. I received the Dell 4600 10-days ago and set up a home network with a Gateway desktop. Both computers use Windows XP and connect to the internet via a NetGear Router. All was well for two days, both computers accessed the internet, shared files and the Dell could print using the Gateway's printer. On the third day when both computers were started, the MyNetwork Places icon on the Dell was gone...the Gateway had the icon. The Dell had no references to the existence of the network connection to the Gateway. However, both computers had the IP Addresses to the router and both could access the internet. I tried the Network Wizard on the Dell three times in order to reestablish a link...failed. Since both computers have a 1394 bus, I checked to see if it was bridged into the LAN...it wasn't. I went to the Dell live chat...their solution was to Restore the System. I have not done that yet...I would like to know why this happened in the first place. Any advice will be greatly appreciated