there has to be some form of indication on the router of brand and model number, why dont you post up everything on the router, see if we can figure it out. oh, and who is your ISP?
you need to be a little more clear about what happens when you connect the laptop with the cable please, the work offline message appears when you try to use internet explorer and what? you can or cant get on the internet? also, did you make sure to turn off the wireless when you hardlined the laptop?