The "LAN" is the Local Area Network, the network that all of the computers are connected to. What you should have in the Network Connections folder is the "Local Area Connection", which is effectively the PC's network adapter. As this is not present, have a look in Device Manager to see if there is any indication that there is a problem with a Network Adapter, or possibly an Unknown PCI Device. A problem will be shown with something like a red cross, yellow "?" or yellow "!"
If this turns out to be the case, it will probably be necessary to reinstall the adapter's drivers.