Well, it will make the bug hunt harder then. 
First make sure your cable is at least cat 5e or better and that it is working.
Next check if the leds start to turn on or blink at the ethernet port on the RPi when it is turned on and physically connected to the router.
If there is no lights, then check that the router port is working by connecting another device with the same cable.
If that works, then it sounds like your RPi might have issues with its ethernet port and you really should get a monitor cable then.