It's hard to picture what you are describing, but I'll give it a try.
You have a laptop that for whatever reason you need to hardwire. You hardwired that laptop using cat5e and a MoCa adapter (small rectangle that converts signal from coax to ethernet cable). You see a communication attempt represented by the activity light at the "port" either laptop or MoCa port doesn't matter.
My GUESS is that your laptop is not receiving an IP address from the router. Check the MoCa adapter has both Power and Coax green lights ON. Coax light means it's connected on the other end to a router (hopefully), but it doesn't guarantee internet access if there are hidden splitters in the coax path before reaching the router (as those splitters are one way and could be installed backwards).
First, make sure that ethernet cable from the MoCa adapter can provide an IP to a different laptop/PC/TV. If another device doesn't get internet then you have to start troubleshooting.
So, if you are 100% sure that MoCa adapter is properly allowing the router to communicate and assign an IP to a different device then your laptop's network card is defective, or the cat5e cable is bad (maybe 1 of the 4 pairs is shorted), the ethernet port pins are bent, or your network configuration (less likely option) is bad.