Wired Keyboard not working properly In Chrome I often toggle between open tabs using Ctrl + tab to go forward, and Ctrl + Shift + tab to go backwards.

For some reason, I can't get the reverse navigation working (using Shift) when using this keyboard. It does work if I use the key combos directly from my laptop's keyboard, however. It's also not working in Messages, to go between conversations.

My Apple wired keyboard (full size with number pad) is plugged into my 30 inch Cinema display, but to be honest, it still doesn't work if I plug directly in to my laptop.

Any ideas?

Update: On both my internal laptop and wired keyboard, I've remapped the Caps Lock key to be the Control key, and vice versa. If I restore defaults, the tab cycling is fixed. If I set the Caps Lock key back to being the Control key, and try to cycle backwards, it breaks. Just confirmed the same is true in Safari. And, no matter how I modify the keys of the internal keyboard, cycling is perfect.
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.