without knowing the details of the computer the Ethernet card could be built into the motherboard, or it could be a operate item. Although most motherboards these days do come with Ethernet hardware built in, it cannot be taken as read.
The easiest thing to do is download an run SIW (software Information for Windows). Look under hardware and netwrok adaptor. This will tell you what you have.
You can if it is built in or a separate card by looking at the connector in the back. If the Ethernet connector is near the video, USB and other connectors it will be built in. If it is separate in one of the expansion slots, then it is an add on card.