Smoky:
1394 FireWire is a connection that is more geared towards MACs. It is also popular on external storage devices. So this connection, regardless of connection status, will not have any positive effect on your LAN connectivity.
You definitely need to have a Local Area Connection object if you are going to take advantage of your hardline connection over Ethernet. Ethernet being the hardline connecting your PC to your Router. This uses RJ-45 connection terminals on the end of the cable. It looks similar to a telelphone connection cable, but having more twisted pairs and pinouts in the cable and on the connection jack itself, its about 1.5 times the size of a twisted pair telephone cable.
If you are connecting your PC to your Router via Ethernet cable, you definitely have the appropriate Ethernet PCI NIC card on your PC as well as within your Router. What you are probably missing is your Ethernet NIC driver for your PC.
I would start with the Computer Management console and determine if you have any devices present on your PC for which there are no appropriate drivers installed by doing the following:
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right-click My Computer >> choose Manage
This will bring up the Computer Management console. From there you will want to select the Device Manager in the left hand pane. You can also call up the Device Manager by doing the following:
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click Start >> click Run >> type devmgmt.msc >> press [Enter]
What you want to do within the Device Manager is right-click on the Local Machine, which will appear as a computer icon at the top of the device tree. Then select Scan for hardware changes. This will poll the hardware devices present on your PC which are present. Devices which do not have a driver installed for them should appear with a Yellow icon with a "?" symbol within them. You may get a generic device such as "PCI device" with the Yellow icon with a "?" symbol in them.
If you are able to connect an Ethernet cable from the PC to the router, but you do not have a Local Area Connection connection object in the Network Connections applet, that would tell me that there is a PCI device (Ethernet NIC) present which does not have any recognizable drivers installed for it. The cable is connecting the PC to the Router. However, the PC does not know how to initiate the Ethernet NIC (PCI Device or card).
Check into that and then post some feedback; we'll go from there.