Can a 802.11 type linksys router work with an "always on" cable connection?

I'm trying to hook up our old DSL router to use with our new office location's wall-socket cable connection that is shared by the building -
if i cable directly from wall to PC it works peachy for this one computer, so the connection is working...
but if i plug from wall socket into router, then router into PC it doesn't work -
could the speed be too great for the 802.11 or what? what could I be overlooking?

I'd advise you completely reset the router to factory specs and try again. The other likely cause of this is that the cable modem has issued a DHCP reservation for the computer and thus won't hand out that same address to the router...so clear out the config on the router, leave NOTHING plugged in to the connection overnight, and try again in the morning.

Check the ports that the wires are going into your router. Your router might be dead too. Check that it powers on and it works somewhere else.