I put them on the counter, put a plate, fill it with veggies, and they come running. They won't eat veggies inside their cage. They believe its an "out of the cage" food and seeds and pellets are "inside" foods! LOL. When I introduced veggies to them, I would be holding two pieces of broccoli. I would take a bite out of mine, say mmmmm and act like its really yummy, then give them the other broccoli. They didn't try at first, but they eventually decided to take a bite and have loved it ever since. Try not to mix veggies at the beginning. Only start with one, so they don't have too many things to suspect. Its best to start with broccoli because most birds find it the most tempting. Maybe you can put them on a table or something and put some in a plate in front of them. My birds love to snatch peas out of my hand! Its so cute! LOL

Good luck! Glad to here your parakeet started coming on your finger. That's a good sign. Just continue to work with them, and lessen their cage time everyday, so they get to experience their freedom in the house. My birds are like practically never in the cage. They have certain "resorts" where they always go and sit outside of the cage. They only go in when they feel like it, and their door is always open when we are at home. Now that your parakeet started coming on your finger, I hope we can see a pic of him.