When you replaced the old computer with the new one did you restart the router or modem or did you just unplug the cable and plug it into the new one. Can you tell us what you have , router, modem or both ?
When doing any changes like that you should unplug everything ,wall sockets , cables everything . Then one at a time starting with the modem plug the power in let it lock up with all the lights on and not blinking except the online activity which will blink once the computer is connected to it. After the modem if you have a router plug in the power and turn on and let that lock up then plug in the cable to your new computer and turn it on and you shiould be good to go.