If your dad wants your old router so that he can connect wirelessly rather than by Ethernet cable then if its the same laptop and the same router that worked ok before then there should be no problem, the only thing to note is that a Virgin modem "remembers" what its connected to so when you connect the router for the first time you must power the modem off so that it forgets what it was connected to. The sequence is as follows:
Power everything off.
Power up the modem and wait about one minute for it to boot.
Power up the router and wait about a minute for it to boot.
Power up the laptop.