Keyboard stops working some seconds after start

Today I turned on my laptop, a HP Pavilion G4, to find everything working as usual. But after some time, I found out some keys could not be pressed at the same time, specifically Z and Q, later it included every other number or letter on a vertical row, except the function keys. Later, and horizontal line stopped working altogether and suddenly it was the whole keyboard, except the function keys, of course.

I tried turning it on and off, which solved the problem, at least for a time, before it stopped working again. Does anyone know what's wrong? I am very sure it's not a physical problem.