Swap the ethernet cables PC and Roku. If the Roku still fails using the PC cable it's not the cable.
Update: I failed to read through the thread. Sorry you're way past my suggestion.
No need for second computer to wire a second roku. Your router most likely has four LAN ports, each can run to a networked device, be that a printer, roku, webcam etc. But, as long as you get adequate signal you should have no issues with streaming ambient sound for sleep.