If you are catching her out eating, she is not broody, she just likes to lay somewhere else. Go out with your coffee in the morning, and listen..... take a chair and a book, but you should find the nest. If you want her to go broody, just leave her be, for a few days and see what happens. But if you find the nest now, you will know where she is.
Chickens really don't get sad, but if they are broody, they can sit for an amazing amount of time as in several weeks. If she is truly broody, either live chicks will work or fertile eggs, I've done both. If you use live chicks, wait till she has sat on the nest for at least 2 weeks, go down in the dark and just set the day old chick on her back, and the chick should just disappear under her. Her voice will change when she starts to feel the chick move and hear them peep. If she is not truly broody, she will kill the chicks. You can't make them be broody. An advantage of getting live chicks is that you can buy sex linked chicks so you know you are getting hens.
Or you can slip fertilized eggs under her, wait 20-21 days, and chicks should appear. Generally anything more than a 50% hatch is pretty good. One should mark the eggs with a pencil, and occasionally check for another hen's eggs getting in the nest. Too many eggs, and none will hatch as it is hard to keep them at the right temperature. Of those that hatch, you can expect about 50/50 males and females, but it can be very one sided, where you get mostly males or females. You kind of need to have a plan for the extra roosters if you go this route.
Mrs K