As Gdkitty has indicated, the CGN 3 appears to have issues connecting to a 100mbs device, which is what is contained on your motherboard. The Realtek PCIE x1 LAN RTL8105E contained on your motherboard only operates at 10/100 Mb/s, so if you are paying for the 250Mb/s service for this computer only, you are wasting money. Even running perfectly, you would still only be running at 100Mb/s max. If you have other faster devices that you are using, its not such a bad situation.
So, you have three choices:
1. If you want to save money and reuse your existing processor and video card, find another motherboard that will support your current processor. Your motherboard appears fairly recent but limited in terms of memory and PCI slots, so its probably possible to find another board that will allow you to keep the processor and which shouldn't be terribly expensive.
2. Buy and install a Gigabit PCIe Network Adapter. This will run anywhere from $15 to maybe $45 depending on what you buy. Your motherboard only has two slots, one of which is taken up with a video card. If the other slot is open, buy a PCI Express 2.0 x1 network adapter. The x1 requirement reduces the number of choices that are available for a Network Interface Card. If this slot is already filled with another x1 card of some type, you don't have any choice but to install another motherboard.
3. Leaving the most expensive as the last option: Replace the processor and motherboard, or buy another pc altogether and keep your current pc for purposes other than gaming.