I have seen it where a "shorted" or dead keyboard prevented a MacBook from booting; even using the power pads on the logic board, after the keyboard was unplugged the computer worked perfectly fine.
However, since you know you spilled oil, and some keys aren't working properly, it's safe to assume that the logic board has liquid damage, and I bet it will need either a cleaning which most placed don't do, or a replacement along with a keyboard replacement,