If you have an always-on broadband connection such as DSL or Cable, then all you need is a hub or a switch (get the switch) and you'll then have two PCs sharing the connection, independent of each other.
Possibly, your provider may use "MAC address identification" (I don't know the proper technical name) IOW, whatever NIC you used to login the VERY FIRST TIME you got the DSL, it only allows that NICs MAC addy or a clone of it😉 to access the network.
Roadrunner is like that. However, my router supports MAC cloning. 😀 Long ago, I used "this" NIC to access RR for the first time. I set the router to "clone" the MAC addy of the system at IP xxx.xxx.xxx.xxx <--internal and *boom* instant clone.
The NIC is long gone, but as long as I don't reset my router to factory specs, I'm good to go.
good luck. 🙂