Setting up internet over coax for Steam Link

[InVinoVeritas]

I'm trying to figure out how to get a wired connection to my new Steam Link using internet over coax (either MOCA or DECA). The problem I have is that my modem and my router are nowhere near each other, so I'm not sure how to make this happen.

Here's the setup and what I want to do, maybe someone here can help:
1. The cable line comes in to the basement, where it is plugged into the cable modem.
2. A network cable runs from the modem, halfway across the basement, and up through the floor to the living room, where it plugs into my router, which is then used to wire a connection to the PS4 and my PC.
3. The Steam Link is on the far side of the basement, opposite where the cable comes in. However, there is a coax line that was installed there, so I am thinking I can use internet over coax. The other end of that coax cable ends near the modem on the other side of the basement.
4. Ideally I'd like to do all of the work around the modem, since I can't easily move the router because it's being used to wire the PS4 and PC. Is there a way to do internet over coax without it going into the router first?

Thanks!

[DirtyCamper]

Usually the cable modem is the router. In some occassions one can choose a cable modem to be a cable modem and use a your own router (the cable modem acting as a bridge).
To be clear upfront: you cannot re-use your coax cable.
What you can do to clear up your cable problems is to have cat 5 cable running everywhere, and on junction points just put an intelligent switch that supports vlans. You can put a specific port in a specific vlan (virtual lan) and designate 1 port as a trunk that bundles all virtual lans over a single cable to the next junction. For instance: you can connect your cable modem to a vlan called wan on 1 switch, have a trunk to your router, and connect the wan port to a port configured for the wan vlan. You connect your private side of the router to a port configured for the private vlan, and you can have that back near your modem. Or anywhere else you want.
You can use the netgear GS108Tv2 or (preferred) the GS724Tv4, both fanless and low in power usage.
Any switch with vlan support should work, but I have this working: internet (2x, I have 2 modems and 2 providers): vlan wan1 and wan2 on a GS108Tv1 trunked to a GS724Tv4 trunked to a D525W intel mobo which has a linuxvserver doing firewalling to private lan 1 (actually a lot of lans), back to the GS724Tv4, back to the GS108Tv1 trunked to another GS108Tv1 connected to the steam link.
The stream crosses pc->2x GS724Tv4->2xGS108Tv1->steam link (4 switches in total).
Not only that: the pc is trunked to the GS724Tv4 because the steam partition is on a fibre-channel-over-ethernet disk on another vlan, which goes to the center GS724Tv4 and on to a FCOE server (a thecus N4200eco with plain debian and some magic installed).

[LadyLoo96]

I am trying to connect my SteamLink using internet over coax (either MOCA or DECA). Currently I am running a 30 foot cable from my router in my bedroom to my Steam Link in my living room. The Steam Link works when I have it plugged in straight through the router via ethernet. When I try using internet over coax (since there is a coax port in the living room) it picks up the network but does not pick up my computer. The coax port does work since I used to have my router plugged in there. Looking at my router, it doesn't even pick up the Steam Link even though the Steam Link has an IP address from my network. I have gone into my router and have enabled pinging. My computer has sharing open to the network.