I am not sure what is going on with her. Is she just broody do you think? Is she grumpy and does she peck at you, refusing to get off her nest (broody)? Or does she appear lethargic and ill? If she is ill, then you may wish to check these basics out:
Check her crop in the morning to make sure it is empty (not sour crop/impacted). Check her abdomen to make sure she isn't puffed up like a balloon.
Check her poo. Check her to see if you can feel an egg (wear a glove and use veg oil) inside the vent that is stuck.
I am not sure of the significance of the blood/goo. Chickens who have an egg stuck will often pass just white urates as the poo won't pass but the urine will. Of course if an eggs is truly stuck they usually will pass on (perish) in a couple of days I have read. I am not sure about the stool you saw.
Also, chickens can have internal problems such as peritonitis (egg yolk periotonitis), cancer, and other things that make them feel bad, as well as infections. It is very hard to say what is the problem.
Additionally, mites/lice and worms can bring a chicken down as well, causing them to be lethargic.
Make sure she doesn't have mites/lice/worm problems.
I hope this helps. I don't know how else to help.
Here is a general link by symptoms:
http://www.apa-abayouthpoultryclub.... SYMPTOMS FOR DIAGNOSING POULTRY DISEASES.pdf