Depends on the switch, and even then it can be tricky. 
Some switches have autosensing ports that can connect a switch to a switch with a straight or crossed cable. If your switch doesn't support autosensing, you'll need a crossover cable. I would be suspicious of the crossover cable. If it's a straight cable, try plugging it directly into the xbox to see if you get a connection light. 
Try to connect everything with known good cables in the same room. If it all works, you can narrow it down to your cables.