Well the options that are left are limited so let's go through this one more time:
1) Have you tried different ports on this router.
2) If this router has Wifi, have you tried to bypass all these issues and get a USB Wifi adapter to use instead?
3) Do a full wipe of the drive, reinstall clean copy of Windows 10 (I am assuming this is a 'off the shelf' copy of Windows, not from a Dell, HP, etc. previously purchased computer your upgrading correct?)
4) Install from the GigaByte CD all the drivers and applications
5) Then use the included GigaByte Update client (look in your Start Menu for the GigaByte folder), and see if there is any BIOS / other updates?
6) Use iOBit Driver Booster to make sure all drivers are up to date.
7) Go to Task Manager click on Performance tab, Select Networking, and take a 'screen shot' and post it here.