There could be a number of possible issues, but all not good. If she has stopped eating, the swan needs to be seen by a veterinarian experienced in waterfowl.

Because most female swans lose approximately 30% of their energy/weight while nesting, it is very important that she gets nutrition and quickly. She may have developed a neurological problem from a nutritional deficiency.

She may have egg impaction in which part of an egg is still inside and this can be lethal if not treated quickly.

Could she have been bitten by a snake or other animal while on the nest?

If she continued to sit for so long in one position, she may have pinched a nerve or done incurred some other damage to the legs in which she cannot stand.

No matter what the problem, she needs to be seen by a veterinarian, placed on supportive care (tube feeding 2-3 times a day until she begins eating on her own), shot of B12 (one dosage to help her appetite). She may be dehydrated and needs an I-V drip to restore fluids.

She also needs an x-ray to see if she does not have egg impaction, if she does, then the egg will need to be removed and she needs to be placed on an antibiotic.

She needs to have her blood drawn and if an infection is present, treated with antibiotics or other supportive care.

If she has to go to the hospital, she can take her cygnets with her if there is room so that she does not get depressed. Otherwise, you will need to catch the cygnets, placed them indoors, feed them throughout the day (drop lettuce cracked corn and poultry layer pellets in a shallow pan and let them eat from the pan. ALL FOOD must be under water so that the do not choke.

Let the cygnets swim in a small tube (With you always near to make sure they do not climb or hurt their legs or feet. Let them swim about 10 minutes per day 3 times a day so that they strengthen their feet while swimming and learn how to be in water.

Once the mother returns, try to introduce them back to her. Make sure there is no aggression. If no aggression towards them, they can be placed with her and she'll do the rest of the teaching. DO not leave them with the male parent because there are no guarantees that he will watch over them. This is usually the mother's role, not the dad's. However, it would be better if you could leave them with him. See that there is no aggression on his part and he is caring for them. If he starts showing aggression or abandonment, you will need to raise the cygnets without the swan parents. The Regal Swan