Wired Keyboard not working properly
If the Shift key works in normal context, and if the same combo doesn't work in say Safari, then I'd think the keyboard hardware has an issue, or the keyboard combination is mapped to another function in Keyboard Shortcuts.

I mapped the combo to Show Launchpad and experienced the exact same issue.  Shift works, Ctrl + tab works, but because I mapped the combo elsewhere it was no longer available to apps to use, and Ctrl + Shift + tab failed in Chrome and Safari.

If that is not the case, then its remotely possible that the keyboard is faulty, but since I would expect other combinations to fail if it were faulty, you haven't mentioned any and I assume that none are.