I have been currently on a 500calorie or less fpr almost 3 weeks I just got off it 3 days ago, and since than I have no appetite an I have not had a bowel movement just little ones. In those three days I have ate, 4 crackers and juice

Well that wasn't very smart. Why were you essentially starving yourself? Thats going to make you sick and not do ANYTHING good for you. Its extremely unhealthy to do. There is no possible way you were getting sufficient nutrition while consuming so few calories.

Obviously its a direct result of your attempting to starve yourself. You don't put much in...there isn't going to be much coming out.

You weren't just lacking nutrients. Your body was burning your wanted body mass (muscles and connective tissues) as well as unwanted fat. Your bones and teeth were losing mass too. Everything suffers when you starve, from hair and eyes to kidneys and liver.
FASTING is different, and is done in shorter duration, and you can't just leap into something like this without knowing what you are doing. It would take all day, so find a site about it.
(And as smoothy said, there isn't going to be much coming out. You didn't eat enough, and what you ate was used as much as possible.)
If you truly got constipated over 3 weeks, cook some rice (the 15 minute kind) and some freshly minced broccoli (for 3 minutes). Add a little steamed chicken for protein.

That type of diet can have serious effects on your health, It is one of the worst things you can do.

Start back on a real diet and proper meals,