Your symptoms sound more like the modem is confusing the router than the router being dead. As it stands now, your computer has an IP address assigned by the modem, and the PS3 has one assigned by the router-but the address is the same because the router wasn't connected when the modem assigned your computer that particular address. Since the router doesn't know that address is "taken", it went ahead and assigned it to your PS3.
I think first you should turn your modem and router off and let them sit for a minute (time it). Then plug the router back into the modem, turn the modem on and wait for a timed minute for it to initialize, then turn on the router and let it initialize for a timed minute. What this should do is get the modem to see the router, connect to it, and provide a full connection through the router to the Internet.
A "dead" router will either not show any lights, show a steady red light, or at least not allow computers to communicate with each other through the wired switch portion of the router.