If you're connecting two computers directly, you need to use a *CROSSOVER* ethernet cable. Normally, if you don't, you simply get the "Network Cable Unplugged" indication.
As your laptop is connecting wirelessly to the internet (the router), it is the Wireless Network Connection on which you enable "Internet Connection Sharing". When you do this, Windows will configure your Local Area Connection (the adapter with which you connect to the second computer) with the IP address 192.168.0.1 and Subnet Mask 255.255.255.0. The "client" computer should be set to get its IP address automatically, which it does by DHCP from the "host" PC.
Because Internet Connection Sharing operates in the 192.168.0.0 Subnet (IP address range) it is important that your router doesn't also operate in this range, i.e. its own address must not be 192.168.0.1 and it mustn't allocate addresses in the range 192.168.0.2 to 192.168.0.254. If it does conflict, its own IP address needs to be changed so that it has a different third octet (number) such as 192.168.1.1 or 192.168.2.1 etc.