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It's unlikely that the original and replacement modems both have a fault, so I'd start troubleshooting elsewhere.
You are completely disconnecting the USB lead from the modem when you swap to ethernet, and powering the modem off whenever you attempt to swap over.
Make sure you have current drivers for the ethernet card in the PC, and that the ethernet is enabled. Everything should be set to auto detect (IP, etc) The modem should assign this. Sometimes having the network drivers for USB loaded can mess things up - try deleting that. Have you a different ethernet lead you can try as a swap.