2. I checked 15 pin of lcd on CRO it shows correct +5V all the time.
What could be problem??
Pin 15 is the Anode of the backlight LED, pin 16 is the Cathode, if you have connected 5v and gnd directly there, you're shoving 5v through that LED without any current limiting.
The backlight led in these usually has fairly high forward voltage (4.2v or some such) and current capability (120mA or some such) which will be why it has survived thus far, but the added heating and current will be killing it swiftly, which is what you're seeing with it coming-and-going.
Like any LED, you need to current limit it.