My Gouldians layed four eggs. The male sat on the eggs every day and only took short breaks to eat and exercise. The female joined him at night. After nearly 3 weeks, they both abandoned the nest. When it was clear that they were not going to go back to the next, I removed the eggs. I gently cracked an egg to see if there was a chick inside. Sure enough, it moved! I felt terrible and put the eggs back! They still won't take care of the eggs and they're not hatching. What went wrong? I'm so upset with myself for doing that :(
Try not to feel so bad. It has been historically hard for beginners to find reliable answers to questions involving breeding Gouldians. If the parents abandoned the eggs, I suspect that something more was wrong. The good news is that your pair did breed and produced viable eggs.
Now it's time to think about what could have made them stop brooding the eggs. I start counting the morning the first egg is layed as one. On the 10th day, I open the nest box again for a quick penlight candling and count of the eggs. If they are viable, I will see lots of little red blood vessels inside the eggs. Looks like a tiny, tiny red road map inside. I don't bother the nest again until I reach the 21st day, hear peeping or unless I see signs of trouble from the parents.
To breed successfully the birds need 14 hours of full spectrum lighting, temperatures between the high 70's and the low 80's, finely chopped hard boiled eggs, (I mix my eggs with a dry eggfood), serve a small amount of that as early in the morning as I can along with fresh Romaine lettuce. There are lots of other dark green veggies that they will eat, but that's a favorite here. In other words, try to recreate the environment of an Australian springtime for them.
Best of luck in the future, Jeanie