When doing network troubleshooting - always start with the simple and easy stuff first.
Where your and his pc plug in - swap those ports. See if his works and yours stops. If it doesnt change anything, move his pc close and use your rj45 cable - does it work now? If so - bad cable - and yes that happens. Also - hook up your PC using the 50' cable just to verifiy its good. Try other ports as the one he is trying to use may be bad.
Make sure the ethernet cable from your router is plugged into the uplink port on your switch. If it doesn't have an uplink port listed, use port 1 as that is sometimes used as the alternate. However, since one PC is working, its doubtful thats where the issue is.
Ok - now that the really easy stuff is done - are you guys using DHCP or have you assigned static IP's to the computers? Check - because you both should probably be using DHCP. He may be set to static and not know it - and thus his settings are way off what they should be.
Next, disconnect the switch, hook JUST his pc up directly to the modem - does that work? If not - then he may have a bad NIC or the wrong drivers to make the network adapter function. This will at least isolate the problem to the machine vs a true network issue.
Lets assume NONE of this pointed at the problem - then you will need to telnet/hyperterminal/web administrate the modem. That switch is what you call "unmanaged" - meaning its not "programmable" in any way - so the problem won't be at the switch unless there is a problem with the device. Most modern modems use a simple web inteface to adminster them. It could be that the modem is set to DHCP - but only has a single address defined as issuable - meaning it can't give his pc one. Get to this point and then let us know where you are - because I am to lazy to type more on this track if its not needed!
