Disconnect Old Desktop from Arris TG1682G And It Still Works with Just Laptops?

Our desktop is nine years old and had Windows 7 so it is now "dead." We had it hooked into the Arris TG1682G as it didn't have a wireless card in it. We now use one PC laptop and one Macbook laptop. Can I just remove the ethernet cord connecting the old desktop and the Arris will still work? Or is it somehow programmed into the old computer's system? Will I need to have a technician come out and make this work with our laptops? Thanks for any help you can give this baby boomer who's trying to figure this out. Susan