My screen broke too....
You need to replae the touch screen digitizer a.k.a the top glass... The reason why you cant put ur password in is because the digitizer is broken and that is what translates your touches into a digital signal.... If it is broken, which in this case it is, then you need to replace the digitizer itself or the whole display unit alpng with the lcd, which would be a safer bet as the lcd and digitizer are fixed together....