Well firstly the problem is most likely in the router setup. Have you setup the router correctly with a wired Computer? But most likely it is a connection issue with your LT and the drivers that are installed in the basic Windows installation.
Do you have permission to use a wireless router at work as well? If these are not configured properly they will allow access to the Internet but not the network and then if some stranger finds the hot-spot that your wireless router is putting out and downloads some Kiddy porn of bomb making material you will have some very hard questions to answer. Which because you do not know the answers you can not answer.
But firstly open the control pannel and click on the Windows components and install all the networking drivers and file sharing protocols as well and some of the other un installed things in XP. If you have SP2 installed un-install it unless you have an OEM version of XP with SP2 on it in which case you up against it from the start anyway. Next open My Network Places and see if your LT sees itself, if that isn't happening there are problems with the LT as it should at the very least see the Shared Files Folder but because of poor setup or conflicting programs many do not see.
Once your LT sees itself you can then start to work on the wireless connection but as you say you can get an Internet connection already the wireless is working properly but your LT isn't being recognized by the system for some reason.
Or depending on exactly where you have placed the router all of the computers might be behind it so they will be invisible to you're LT this is what routers are supposed to do. The router should be placed between the Internet connection and network for you to see the rest of the network and the router should be feeding the network as well or you will see nothing at all on the network.
