[Blue Lord]

The router will, unless told otherwise, stop your ports from responding to pings. Someone pings your IP, worst case, the recieve "Port open to connections". As far as computer security goes, it goes downhill from there. Second worst case it responds with "Port's here, but closed". Best case, unless you did something to prompt the ping or have a specific port set to accept connection, it doesn't respond at all.

Which means the hacker in question might aswell be throwing packets at a computer that's turned off.

Add a firewall and a paranoid mind and you're safe as can be, short of *shudder* get rid of your modem.