Yes you can disconnect the coax cables from the splitter the cable company installed. I recommend removing the 4 way splitter completely and connect the cable line that was connected to the input of the 4 way splitter to the coax that goes to your computer with a inline coax coupler , commonly called a barrel because they look like barrels. Knowing that you are intent on doing it your own way I am giving you more clear cut directions , Do Not reuse the 4 way splitter for the antenna unless you are going to actualy and are for real connecting 4 Tv's to the antenna , The reason is --> each time the signal is split - the signal strength goes down. Go to Home Depot or Lowes and get a splitter that has outputs for the number of Tv's that will be connected. You can also get the barrel at Home Depot or Lowes. Here is Picture of a Tv antenna mount that will get the Tv antenna above the top of the roof line with out putting holes in the roof , it is a eave/gable mount ,
http://www.sadoun.com/Sat/Products/Perfect/PVEM1.gif . I know that you are intent on making sure that you do not receive all of the Tv stations to the north and south.