If your parents only have one pc, they don't need a router. The modem plugs straight into the pc.
ADSL modem routers and cable broadband don't mix. Your only hope is to plug the cable from the cable modem into one of the ports of the router and the pc into another and see what happens. Some routers have auto-sensing ports.
You will need to switch off the modem part of the router in its setup pages if there is that option and also decide whether the cable modem or the router should act as the DHCP server (but not both) - probably best to use the router.
Otherwise, you will need a new router.