The "1394 Connection" is *FIREWIRE* and nothing to do with your ethernet connection to a Router. If the PC's network adapter is properly installed, there should be an entry in the Network Connections folder for a "Local Area Connection". If this is missing, go into Device Manager to see if there is a problem indicated by a yellow "question" or "exclamation" mark, possibly due to to the drivers not being installed properly.
Your Vista laptop's inability to connect "wirelessly" is not likely to be related. Try deleting the existing wireless 'profile' and then go through the procedure to connect again. Open the Network & Sharing Center, then click the link at the left to Manage Wireless Networks. In the window that opens, highlight your wireless network and click the "Remove" button. Then connect again when a new 'profile' will be saved.