If it’s not showing up on your router, then either there’s a fault in the interface between MyCloud and router, or there may be an IP address conflict. If you’ve tried a different cable, and different router/router port, then it does sound like your suspicion of broken Ethernet port on the MyCloud is likely.
What are the LEDs on the MyCloud’s ethernet port showing?
Have you configured a static IP at the MyCloud end? Is that within the router’s DHCP IP allocation pool? Given that you have performed a 40-second reset, this should have reverted to DHCP, so that question is probably moot…
If you don’t have a backup, and you need to recover data, read this thread:
