The ethernet cable that you're using might be an issue, but it's only one of the possible reasons why there's no connection when the computer is directly connected to the router. Other reasons that I have in mind are Ethernet port issue, Wireless connection, and TCP/IP configuration.
Here's what I'll do..
I'll turn off first the wifi switch, bypass the router then try to go online, if it works, there's no issue on the cable or the computer's port. If there's no connection, verify the Local Area Connection, it should be Enabled. Then verify the IP Address if it's Valid, if not, go to Local Area Connection window and choose repair/diagnose the problem. If repair completes successfully, attempt to go online. If repair fails, verify TCP/IP settings are correct. If there are changes made, reboot the computer and try to go online. If no access still, check Device Manager and make sure that the Network Adapter has no error, if there is, you need to contact a technician or the computer's manufacturer. If there's no error on the Network Adapter, run the ping command. If ping result is okay, the connection is just there and attempt to go online. If ping fails for the Domain but not on the IP address, it's a DNS issue and needs to hard code it manually or just run release/renew the IP address and restart the computer. If still there's no access, replace the cord and try to go online. If everything fails, consult a local technician or computer's manufacturer.