Your body AND mind need to change. Your body sounds like its had a lot of yo-yo dieting going on, and its out of whack.
Start drinking lots of water. I mean LOTS. Drink enough water a day so that your pee is clear most of the time.. I would cut out soda, this include diet. Sugars just make you feel hungry.
Next, eat LOTS of small meals a day if hunger is making getting through the day that much harder. This also goes hand in hand with your calorie limit. 500-1500 calories a day is not enough for your body. I don't care what your doctor says. Your body is VERY confused right now. 500 calories a day will put your body into starvation mode by the way, which can lead to binges. How do I know this? Back in the day I decided I was going to starve myself. Lost 30 pounds in 2 months and then lost control, started eating everything in sight for about 3 months. I gained 40 pounds back even after I started to eat the right amount of food to maintain.
Don't even consider gastric bypass surgery. In your case that would be stupid since you claim that no matter what, you are hungry, even when you can feel your stomach being full. If it truly is physical hunger, then you need to learn how to deal with it emotionally. You need to learn how to live with it. Many people out there live in severe pain on a daily basis, yet they can learn how to block it out.
You have to stop cutting your calories to an extreme. You have to give things time. You can't go from eating 4-5k calories a day down to 500 calories a day and expect to not feel hungry. The same applies to cutting down to even 2000 a day. You wouldn't bench press 20 pounds for a few months and then just increase your weight to 300 pounds one day. Your body wouldn't have the strength.
Everything takes time and adjustment. That could be years. You are so physically and emotionally used to eating 5k calories a day, its going to take time. Don't go on a diet. Change your eating habits for life, follow the same plan for the rest of your life. You can't give up just because you feel hungry. EVERYONE on this forum that has lost weight has experienced being very hungry. And EVERYONE has struggled with it. Go read through some of the diaries, there will be entries where people yell at themselves for giving in. A lot of this has to do with will power and you need to realize this. If you don't eat enough and learn how to live with this problem you will never keep the weight off by the way. Seeing a therapist or nutritionist could help as they could teach you coping methods.
Get tested for gastrointestinal diseases such as celiacs if you think there is an underlining condition to blame. Celiacs aren't just underweight, its been discovered that many are overweight, because their body thinks its starving and they have an appetite that can never be satisfied.