IShe is likely egg bound and getting her to a doctor who is experienced with birds, preferably an avian specialist, is necessary right now. You cannot delay!
In the meantime, making sure she gets some plain water with an eyedropper just inside the beak, a drop or two at a time (slowly, not forcefully) may be helpful in keeping the bird alive until medical intervention.
You can try swabbing her vent area with a bit of KY jelly or other lubricant (not Vaseline) - even regular cooking oil is ok in a pinch.
Set her in a shallow pan of warm water (not hot) - this might relax the muscles enough to pass the egg.
You don't have much time - find an urgent care facility and go now. It's far better to be driving two hours to the nearest caregiver rather than trying to wait this out.
She may not only face a life threatening situation here, but this is a common cause of paralyzation in birds. Sometimes permanent.
Egg binding may have any one of a number of underlying causes, including hyperthermia or hypothermia (too hot; too cold). By improving the temperature and humidity in the environment, it could help with the passing of the egg; other causes are malformed egg, poor muscle tone or other health and condition problems in the hen.
There are various methods of treatment that an avian specialist or experienced vet may attempt, but none of these procedures can be executed by someone who isn't highly experienced with the condition; even many breeders would prefer medical intervention rather than chance the loss of the life of their bird. http://www.tailfeathersnetwork.com/birdinformation/egglaying.php
Putting a heat source into the cage may be necessary since a sick or distressed bird may lose body heat. I prefer a non electric source and use rice socks. Also, raising the surrounding temp may encourage a bound egg to pass if this is, indeed, what the problem is.
Use a thick, clean sock and fill it ¾ with plain, raw white rice. Knot the end and microwave it for about 1 ½ minutes. Shake it afterwards to distribute the heat and be sure it's not too hot.
You can layer a thick towel on one side of the cage, secure with clothespins out of the reach of the bird's beak - then clip a heating pad over the towel and set on low. Check often to be sure it's not overheating and that the bird isn't gnawing through. A side attachment like this will allow the bird to move closer or away as needed.
If the bird is bottom-bound, install a heating pad under just a portion of the base, again, set on low.
The rice sock option is far safer and more efficient though.
Cover the cage with a thick blanket, leaving all or part of the front door uncovered for better air circulation, to help keep the bird calm by being able to see out and of course so you can check on it regularly just by peeking in. The covering also helps hold some of the heat inside.
I'm very uncomfortable giving the heating pad suggestion because of the potential for the bird to bite through the bars and possibly catch a part of the heating pad. This is just one reason I prefer to avoid electric sources of heat. Another reason is that heating pads can suddenly become faulty and overheat. If ever using an electric source for heating anything in anyway, please be vigilant and constantly double checking carefully.
Certified Avian Specialist
Cert. Avian Specialist; Int. Assoc.Animal Behavior Consult; Pet Ind. Joint Advisory Council; author