My kitchen lights won't turn on, what could be the problem?
Assuming florescent lights, the most likely cause is a failed ballast. Generally a bulb or socket issue will only affect 1 or 2 lights, not all 4.

Replacing a ballast is pretty straight forward and just requires re-connecting the necessary wires.  Make sure you note the old ballast type, as well as the bulb types and wattages when selecting a replacement.

If it is an older fixture with T-12 bulbs, you will most likely need to replace the ballast and bulbs with newer T8 bulbs that are more energy efficient.