Coaxial to Ethernet Modems (500mb/s v. 200mb/s)

Thank you for your answer, this answered my questions. I have few more for you, if you don't mind asking. I am splitting a Coaxial cable using a 5-2400Hz Splitter, this one RCA DH24SPF, one going to a modem setup to a part of my house and the other directly going to my room through a Cable Modem, would my speed be split in half or would it stay the same. Thank you

So that would mean I need to call my internet company and request that they turn on the second Coaxial cable coming from the ground, unless I can turn it on myself? since the Technicians they send charge quite a lot just for arriving.

We currently have Cox and I am not too sure whether we can make a subnet, but do you know you would do it? Would we call Cox and request that our account will have a subnet, also if we do have a subnet how much money does it add to the total cost 10$-20$? Would there be any speed decrease if we use a subnet, I know using the splitter would slightly decrease but would a subnet do the same too? Thank you for all your help so far!

EDIT: Changed the picture, since it was unclear.
Hopefully this MSI Paint drawing (Sorry for my terrible artistic skills) will help out. We have two Coaxial cables coming from the ground, one is screwed to our coaxial in our house and the other one is not connected to anything and is not live. We know this because we unscrewed the the connected coaxial cable coming from the ground going to our house. Then we unplugged and took our router and modem, then connected the modem to the unplugged ground coaxial cable. Both the router and modem all got green lights, got a laptop out there and we were connected to our network with 6 Bars, so we tested YouTube and Google, both worked. Then we unplugged the live coaxial and connected the second coaxial coming from the ground to our modem, no receiving light turned on and the Netgear was not receiving a signal from our modem, so we tried Youtube and some other websites, just as we expected nothing loaded. Now what I am thinking is whether I can make that second cable live, but if that means that I would need to buy a new internet package from Cox, then I wont do it. I really do hoped the picture helped and if you need real pictures of the cable box with everything, I would gladly upload them! Thank you so much for what you have been doing so far!

--------------Optional--------------------------------------------------------------

The entire reason why I am doing this is because our house is fairly large, and I am currently connected to our network by ethernet cable which is connected to our Netgear router. The issue is the Netgear is by a loud 50" TV blasting Fox News into my ear and there is a very loud cooler to the right of me, and I have trouble focusing on my scripts for my AP Computer Science class and when I skype my friends they always yell at me that my background is annoying. My room is about 120-100ft away from all the hardware for the internet. I told my dad just to buy a 150ft Ethernet and run it to my room; however, he does not want to run a cable through our house (I have no idea why and it's much cheaper). He then told me that the cable box was about 5 feet away from my room which it is, so then I looked into to it and it was possible to drill a hole through our flimsy wooden window to my room. Then we would just run the coaxial cable through that hole, and buy a second Modem, but from what you have said splitting a coaxial cable to two modems is not possible wo/ having to pay. I know all this might seem like a way over the top thing for just me just being able to focus more and not get yelled at by my friends, but I just don't want people to begin to think I am some needy kid.