they may be defective. i would suggest taking a toothbrush soaked in alchohol to the stick modules and try to clean it out as best as you can. if that doesnt help then you are looking at replacing the modules all together.
umm its a little tricky. id assume if you changed the battery and that didnt help, i would reccomend changing out the charge port/led circuit board. and if that doesnt get you fixed then it is the main motherboard in your controller.
it seems to me like it would be the motherboard, but since its nintendo its the screen. all of the ds's do the same thing when a screen is faulty or loosely connected Update (03/05/2017): !confirmed! it is the lcd screen that causes the fading blue light on the wii u game pad i just did a repair on one with the exact problems listed. i attempted a battery and motherboard swap, but i did thescreen swap and bam fixed it.