I am really sorry for your trouble but let me help you with this.
The information you have provided is helpful for me to have a picture of what the problems but I would like to get some more details to provide accurate troubleshooting steps.
Please try the following steps:
- Update the BIOS of the NUC to latest. Here you can download the latest version:
- Uninstall the current Ethernet driver and install the one provided here:
- Try different Ethernet cables and if possible with a short distance from the router.