I'm not sure what type of network adapter this is, but you can find all the drivers for intel wired network as well as wireless from the following links:
From the above list you can choose which of the adapter is yours and then download the appropriate drivers.
You can follow the steps on the link below to be able to identify the network adapter you have on the system:
Please note these drivers will work mostly for the boxed versions of the network adapters. If the adapter was already assembled into your system before you bought it, you may wish to contact the manufacturer of the system as they may have altered the adapters hence only their drivers will work.
Hope this will help you a bit.
Yes, your LAN connection is built into the motherboard of your computer. Your computer probably came with a CD that has the drivers you need. If you do not have a driver that works, your best source is to get the driver from you computer manufacturer.
From your description, you probably have an Intel(R) 82562V 10/100 Network Connection. The same drivers that work with many of the Intel(R) Ethernet gigabit connections will work with your connection. Try your computer manufacturer first, but the generic driver link below will take you to a package that should work on your computer.