Would doing this work!!? (computer issues)?

i have a router (non wireless) and i connect it to the tower of my computer but when i play my PS3 online i have to switch it and when i switch it i cant get on the internet because the cord to in the tower inst in the router so i cant get on the computer. so if i buy a cable splitter and the ond of the splitter into my router and the put the one to the tower in one of the plug-ins for the splitter and put my other cable for my PS3 in the other plugin on the splitter would it work or fail