<<< the LAN is showing "100.0 Mbps Limited or no Connectivity" >>>
100Mbps is the normal speed for a wired network connection. "Limited or No Connectivity" normally indicates that the network adapter is set to get its IP address automatically, but has been unable to find the DHCP server from which to get it.
I don't know how you have them networked, but if you are using "Internet Connection Sharing" this will automatically configure the Host PC's network adapter with the fixed IP address 192.168.0.1; the Client PC then gets its address from the Host PC which acts as a DHCP server when ICS has been enabled.
The "1394" adapter is a Firewire connection and has nothing to do with your LAN. If this and the Local Area Connection are bridged, right click the Local Area Connection and select "Remove from Bridge". You can do the same with the 1394 connection and then delete the bridge as it is serving no useful purpose. (This is reversible by highlighting both connections, right clicking and selecting Bridge Connections).
With Internet Connection Sharing, the Client should also have an IP address in the 192.168.0.xxx range. If it doesn't (and with Limited Connectivity it may have a 169.254.x.x address) try double clicking the Local Area Connection, select the Support tab and click the repair button. This should force the adapter to renew its IP address. If that doesn't work, there may be a firewall problem preventing the two computers from communicating.
If you are not using Internet Connection Sharing and have been using fixed IP addresses entered manually, one of the computers has lost its settings and reverted to getting automatic addresses.