Both ctrl keys not working

Solution 1:

I had the same problem for months, both Ctrl keys and back arrow key did not work.

I had to reinstall Google Chrome, all keys then started working again.
This was possibly by accident or a related Chrome issue.

Solution 2:

Press alt+ctrl+fn to fix.

I am not sure why this happens, but I was also not able to use both the Ctrl keys and this worked for me. Please find below the related thread.

http://ccm.net/forum/affich-28177-control-keys-not-working-on-laptop

Solution 3:

Did the ctrl key ever work? You mention the keyboard is new, don't exclude the possibility of a manuf. defect.

That being said, there is a definitive way of diagnosing between hardware or software. Try booting to a linux live CD (or any other 3rd party O.S.), like mentioned in the comments. Here's a list of free software that will allow you to make the diagnosis. Ubuntu, DamnSmallLinux, Comodo Live, Hiren's BootCD, Ultimate BootCD

"Almost 100% sure" isn't very certain at all is it? Also, there's no point testing the keyboard using software if the issue is with the same software it question.