Sounds like the Router might be daulty . . what is the history?
With the pc connected to the Router and the router to the modem, try this:
Click on Start . . Run . . type CMD
At the > prompt type type the following command: IPCONFIG /ALL
Note that there is a space before the /ALL, but there is NOT a space after the / in the following command.
Right click in the command window and choose Select All, then hit Enter. Come back here and Paste the results in a message.
If you are on a machine with no network connection, use a floppy, USB disk, or a CD-RW disk to transfer a text file with the information to allow pasting it here.