Have you checked in Control Panel and made sure you show the correct type of keyboard for a laptop?
Have you spilled anything on the keyboard?
I would assume an external monitor would show the same thing, but you might check. If you use the onscreen keyboard, does it behave the same?
I would probably try to remove the keyboard and reseat the plug. But if the onscreen keyboard behaves the same, it is probably not the keyboard itself, but something interpreting the keystrokes.
It does sound like a driver, or a virus, but it might also be related to a language situation.