I Dont no what the tech specs of a cat5e ethernet patch cable is sapost to be. But FYI i used the ethernet cable that came with the xbox (i assume its just a normal ethernet cable) and it seems to work fine.
If you dont have admin rights to the router, that might be your prob. If you do and all 3 pieces of hardware work assuming there not broken. and your router is on factory default(assuming you or someone else didnt break the firmware) and doesnt have MAC address filtering etc enabled... Just plug it in and forward the 2 odd ports above 1000 from this link... http://support.xbox.com/en-US/xbox-l...used-xbox-live
if not working by your description sounds like one of your things is just physicaly broken