Keyboard mis-mapping

I have a weird issue with my keyboard. I have an Alienware m17x r3 running Windows 10 Enterprise 64bit.

The 'a' key does nothing when pressed

The 's' key outputs a '-'

The '-' key outputs an 's'

The 'w' key outputs an 'a'

The No. 2 key on the keypad outputs a 'w'

The 'd' key outputs a '2'

Nothing will output a 'd'

All other keys are fine, including the Shift key for the swapped keys.

In the time I've had this issue, I've reinstalled Windows several times, upgrading where possible. Today, I bought a brand new keyboard for my computer. The issue is unchanged.

I'm using an external USB keyboard right now.

Anyone have any idea what the problem is and how I fix it?