First of all, you need to read the description of EVERY forum section. And read that carefully.
You will know where to start a thread regarding which topic.
PC Components / Configurations
Questions about configurations go here. Strictly Buying Advice - No troubleshooting here. Go through each and every sticky thread of this section and other sections before posting.
Are you buying a PC? No, you are not.
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Now coming to your query, you don't have a Router cum Switch from what I could read.
But good thing is that you have Gigabit Ethernet in your motherboard which means Auto MDI/MDIX.
Set both Ethernet Adapters to "Obtain IP Address Automatically." Google regarding this.
And simply put one end of the LAN cable in Computer and the other end into the Laptop. Unknown Connection will be detected. Configure IP address etc. Google regarding this.
The network should say "connected." Then type "ipconfig /all" in the Command Prompt of both machines to know the IP address of each of them.
Host the server in one machine. Tell the other machine to connect to the IP address of the server.
Also - read this thread:
*www.thinkdigit.com/forum/networking/154756-file-transfer-lan-cable.html
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What I suggest to newbies is, to buy an ADSL Modem + Wifi Router like this.
*i.imgur.com/b6QTc.jpg
In this, all you need to do is - connect each PC to the router either via Wifi or through Ethernet cable. This makes networking easy and also shares the internet among all connected PC.