I, too, have a Gateway NE56R41u with a (locked?) keyboard. You asked how one can still type? I select "Ease of Access" when computer starts, then select the On-Screen Keyboard. Other options include a USB keyboard; and I once utilized Dragon - a talk-type program.
Now, once again, I am searching (11 hours now) for a solution for this keyboard. Why isn't there a super simple SUCCINT solution online, one that makes every "Dummies" publication appear beyond Einsteinian in complexity? My brain cell is overworked and lonely.