Difficulty in establishing a LAN connection

My main computer is connected to a router and cable. My second computer is a new Gateway with built in WiFi. When installed the antenna on it, I got internet without having an adapter. I have an embroidery machine than formerly we connected to the second computer with a serial cable. Since the new computer has only USB ports, we cannot do this.
However, when we bought the emb machine, we got the license for a LAN connection. My manual instructs to connect the emb machine to a router with an Ethernet cable, then another Ethernet cable to my computer. It does not work. Can I connect the emb machine directly to the computer using an Ethernet cable and will it pick up the built in connection?
