Bizarre keyboard behavior

NOTE: I posted the following to the Microsoft support forums but have not yet received a response there.

Since last night, my keyboard has been acting very strangely.

The square bracket keys do nothing when pressed with my left shift key; I can only get curly brackets if I press the right shift key.

However, the opposite is true for the letters z, x, c, v, m, and the comma and period. They only work with my left shift key, and do nothing when pressed with my right shift key.

Using the on-screen keyboard, I can verify that pressing left-Ctrl or left-Shift individually is recognized by the system - but if I hold down left-Ctrl and left-Shift together, it only sees left-Ctrl. Similarly, if I'm holding down right-Ctrl and right-Shift together, it only sees right-Shift, even though both are recognized individually. If I try to hold down left-Ctrl and right-Shift together, whichever one I pressed first is recognized, and the second is ignored. However, right-Ctrl and left-Shift are recognized as a combination, though Ctrl-Shift-Tab doesn't work regardless.

Earlier, holding down Shift+5 and Shift +6 gave me capital M and capital V, respectively, when using my left shift; when using my right shift, I got capital T and capital Y instead. This is no longer true; now, it doesn't recognize that I'm pressing 5 or 6 at all with shift, but it recognizes me pressing each shift individually and the 5 and 6 individually.

Left shift and T don't work together, but right shift and T do. Right shift and C don't work together, but left shift and C do.

The above is not even close to the full list of bizarre working and non-working combinations, but it will do for now.

Normally I'd suspect a hardware problem - maybe I spilled water on the keyboard without realizing it or something. But unless I'm mistaken, that shouldn't stop key combinations from working when each key works individually...

Anybody have a clue what's going on? I am using a Dell Inspiron 15 7000 series, with Windows 8.1. I've tried rebooting, and I tried uninstalling the keyboard from Device Manager with an eye to reinstalling it afterwards, but it just got reinstalled automatically upon reboot.