What you are probably thinking of is what is called MoCa, Multimedia over Coax.
What you first need to understand is there is cable types and there is protocals.
A cable is simply a physical item defined by things like how many wires it has in it, and what frequencies it supports; a protocol is a specific format that data is sent/received in.
Coax is a cable, cat5/cat6 is a cable
Docsis and Ethernet are protocals.
You can use a Moxa adapter to transmit Etherent data over an existing Coax cable. This requires you to have an existing internet connection (typically using Ethernet) to plug into the MoCa adapter to then convert it to be transmited over a coax cable.
If you don't have an internet connection then bottom line you need an interent connection from somewhere.
If your room has its own cable tv account with the cable company then you can get cable internet. If the building owner has 1 cable tv connection and splits it to the rooms then there is nothing you can do to get cable TV unless the building allows you to have your own separate coax connection (and then you will have to pay for TV and Internet through the cable company).
There is no way to just fabricate internet data out of a coax cable that only has TV data on it. You need the cable company to be sending you internet connection (using DOCSIS protocol) over the coax cable that you can then use a DOCSIS cable modem to decipher and then convert to Etherent for your computer.