My hen won't lay or leave the box...

Sounds like you got a broody there. They stop laying, hang out in the nest box constantly, and make a low "boink, boink, boink" sound.

 

When you take her out, does she fluff her feathers up and cluck? She may be broody.

 

Yup, sounds like a broody hen. What breed is she? Some tend to go broody more than other's.

 

She has gone "broody", which is to say; her inner clock is telling her to hatch some chicks. Have you seen the other girls laying eggs for her to sit on? I have two brooding hens at the moment and they both are sitting in the same nest. The other girls squeeze in and lay their eggs and then get up, sing the "I just laid an Egg" song and then go on about their day.
I take them off their nests when I come along and I place them on the ground so they have to go the long way around to get back in the run and they always poop a MONSTER poop and eat and drink along the way.
Your girl will be fine. You don't need to worry. She will not die from lack of food or water.

 

You have a broody hen. Put some fertile eggs under her, and in 21 days your flock will increase.

 

No of course you don't HAVE to get a rooster! It's just her way of wanting to be a mommy but you don't have to let her. Do what the other poster said and take her out of the nest box a couple times a day so that she has a long walk to get back in. She will take the opportunity to eat and drink, and eventually get over it.
I remember when I first got chickens, I spent one christmas trying to keep alive a "sick" silkie who was in a broody trance for weeks. I had no idea about broodiness and seriously I thought she was eggbound and dying! I spent days giving her warm sink baths and trying to vaselene her bum!

 

If you take the eggs and she still wants to sit, make her get out and get some sunshine, even if you have to separate her in a special "broody" pen.

 

Here's a good thread on breaking a broody hen. I use a wire bottom rabbit hutch as my broody breaker, some people like to just let them go until they give up on their own but I don't see the point in letting the hen lose condition and us loose out on the eggs.

If you change your mind and want to add to your flock you could also try to put some day old chicks under her some night after she's been broody for a week or two. Occasionally a hen will reject the foster chicks and then you have to brood them yourself, but I've only had that happen once. The main advantages of giving a hen foster chicks instead of letting her sit on eggs are that you can buy sexed chicks (not 100% accurate, but way better odds then hatching eggs) and that you can get the breed(s) of chicks that you want--or even another species. I let one hen sit on duck eggs (she lost her mind when they discoverd the creek) and fostered turkey poults on another one. I have three more broody girls this week and am going to give two of them turkey eggs to hatch and the other one some two day old peachicks.

ETA: The dang thread on breaking broodies.

https://www.backyardchickens.com/forum/viewtopic.php?pid=2176186