No internet connection on desktop

Hello, I didn't find an answer that addressed my concern ... so I'm asking the question. I have cable modem; desktop computer; router and a laptop. I had not powered-up my desktop for several weeks but continued to use my laptop and had no internet issues. I tried my desktop recently and cannot get a connection to the internet. Still no problem with my laptop. I've turned everything off ... powered back up in sequence ... still nothing on desktop. I've connected the desktop directly to the cable modem and still it tells me the same thing ... cable unplugged. I remember that I used to have a flashing light visible inside the port (on the computer) that connects to the cable modem. That is no longer the case. I've tried to run troubleshooting but it always comes back and tells me the cable is unplugged. I've read some posts that suggest the NIC (not sure what that is) ... may be faulty. Can anyone suggest a way I can check it. This is a Dell Dim4600 (bought in 2004) ... I hate to retire it because it has XP and I love it ... but don't really want to spend money on such an old computer.