For some reason I don't feel very reassured of the repair place that you sent your PC too. They said that you needed a new motherboard, which is fine if they say that and it is not booting up but then when they put a new one in the internet does not work so they ask that you do a restore of factory settings?
Now i could be wrong but does that mean that they changed the motherboard but then continued to use the currently installed Windows to test it?. I would have thought that a fresh install of Windows would have been needed as it is a massive change in hardware.
It looks to me like they then used a Linux live cd (I bet Ubuntu)to boot up your computer to check the board and of course the internet works, as it is acting like a fresh operating system install.
I know that i am new to this board and i dont know if you would want to try this but my advice would be to do a total reinstall of windows and start from a fresh and clean Windows. I am sure you can save any save games for your FM2012 and others to transfer over when the installation in complete.