Second router??

Also the internet system was installed inside the house to a coaxial cable in the wall. Now can that router be moved to another coaxial cable in a different area of the house(ex: to a coaxial wire that was for a tv cable box? Or does the panoramic wifi router have to be started and running from the wall mounted jack location? If this makes any sense lol.

Thanks for the info and suggestions...the issue im having is to run an ethernet cable to the location i want is going to be mostly from inside into garage and around so many walls i would need about 100-150ft of wire and with that long of a wire i have seen that Its not recommended for live gaming. When the door is shut it almost a 1-2 full second lag time and for what i pay for the service and amount of download/upload speed it shouldn't do that. Honestly i had at&t internet lower of a plan and it ran alot fast on my console. So im wondering whats happening. 

i do it with an older netgear router, harwired to panoramic unit, then netgear hardwired to backup pc.

speed is quite a bit slower than both wired/wifi from panoramic unit.