Wireless Router/ Ethernet?

I have my home computer wired directly to a router with an ethernet cable. I have been having issues lately with computers that are hooked directly up to the modem losing internet connection. When I disconnect my home computer from the router and hook directly into the router, the problem seemed to be solved. So I figured that my issue was with the router which was several years old so I replaced it. I just went through the whole set up process for the new router and everything was fine for about 30 minutes and then I suddenly lost internet connection on the computer that is hooked up through the router. When I disconnect from the router and plug my computer directly into the modem, I have internet again.
According to the troubleshooter, when I am hooked up thru the router it is saying that there is a cable that is not connected. I have tried different ports on the router and this is still not fixing anything. Is it possible that my enternet cable is bad??