It sounds like your hen could have sour crop. There are two keys...does the crop empty overnight and is she pooping? You said her poop is runny so at least her crop is not totally blocked and preventing any food through. Here are some suggestions that have worked for my hen that had sour crop. Remember that each bird is different and I haven't seen your hen to know what her crop is like, etc., so you'll have to be the judge of what to do.
If possible, isolate her so that you can monitor her food and her poop. I'm going to try to find a thread and post the link to it where there is information that may help you. If you pick your bird up and she feels like she has lost weight, you will need to do some immediate care for her.
Yes, you need to get this bird to vomit. But, a more helpful way, I think, is to flush the crop. By using a feeding tube and syringe without a needle, inject warm water into the crop. Depending on how full the crop is now, you could inject 60cc+ of warm water. With the water in there, massage the crop to help loosen what is causing it to be blocked and then hold the bird upside down, making certain that her head is always down. If she lifts her head, liquid can pool in her mouth and she may aspirate it into her lungs which could possibly kill her. There is an opening to the lungs in the mouth toward the back of and under the tongue. Flush her a couple of times and try to get as much of the junk out as possible. I held my bird over the toilet so I could see what was coming out. That will help you to know what's causing the problem and you can keep her away from that stuff after she recovers as it may cause the same problem again.
Do not keep feeding the bird anything other than soft food. The food isn't going through so it is only making the problem worse. If she is pooping some, that's a good thing but she needs soft food. I used diluted baby food through the syringe. If she'll eat it herself, it doesn't have to be so dilute. Someone who is studying to be a vet cautioned that using baby food with garlic or onion powder is not good for birds long term as it causes hemolytic anemia. I doubt that you will be using baby food long term but keep that in mind.
I'll paste a couple of links for you. One is pictures of poop so that you can compare your hen's poop to the pictures and get some info about where she is. Another is a first aid site where (if you scroll down) you can see a crop tube set up and instructions. I will also look for a link to a thread here for more info. Keep us posted. We hope you can save your hen.
http://www.chat.allotment.org.uk/index.php?topic=17568.0
http://www.broodyhen.co.uk/ket/fowlnotfoul/1staid.htm
https://www.backyardchickens.com/forum/viewtopic.php?id=442100
Keep us posted and feel free to ask any questions that come to mind.
