Internet connection to computer

My IMac is about 7 years old. Recently I could not connect between the computer and the ADSL modem. I have checked the modem and it is OK. I have changed the cable. I checked the port on the computer and it seems to be clean and norma. This condition happened recently. Need help!e

Call your ISP. They will tell you if the lines (outside and connections, etc) and modem are OK. Time Warner did that for me. Probably time to bin that old Mac, though.

And it still could be the router. As suggested ask your ISP to see if they can check the router and if it is connecting.