Is the router part of the modem giving out an IP? Can you ping (or reach through the browser) IP addresses? (eg 184.108.40.206 for techreport.com) Can you at least get to the admin page for the modem/router?
Have you tried a full reset (not a power on/off -- see the manual). Having done the reset, have you set all the necessary parameters in the setup pages? Hint: you might want to save the current settings to refer to before doing a reset. Bonus hint: if the relative already tried a reset, those settings might be wrong. You may need to consult the ISP (or run the setup disc that probably came with the modem, if that's still available) to get the right settings; every ISP can be different (QWest has a wonky VCI setting, for example).
Of course it's also possible the ISP is having problems, or there's a physical break in the line.