So Loralee have you tried to hand feed this pigeon? Just put some bird seed or even chicken feed in your hand and slowly move it toward it. Give it an extra 6 inches or so of space and see if it will come to you. If that spooks it put food and water in the same place every day for it. If it is watching you it will start associating you with good. It sounds like it has been handled before or is at least used to humans. I am sure it recognizes that you will feed and water it. I am a true believer that animals in need can often sense when a person is willing to help.