BATTERY IS DISPLAYING (NOT CHARGING) -What to do if your Mac Book Pro 13" even if it is on the power source adapter. I have dim all the lights and other energy saver as instructed. Any advice please .

Since this is a 2012 model Mac then it is NEW. You should call Apple and see about taking it in for service. If the power, AC, adapter is connected to a Known Working electrical out let and then connected to the Mac and the Mac is not charging there is a hardware problem with either the Mac or the AC power adapter and onlyu Apple can fix or replace whatever is broken.

Does the light come on in the power connector that connects to the Mac? If not then it is not getting any power. That light is either Green or Amber. Green for fully (and or Almost Fully) charged and Amber when the system is charging the battery. No light means the AC adapter is either not getting any power from the Wall Outlet or the AC adapter or the Mac is broken. In either of the last 2, broken AC adapter or broken Mac, you can replace the AC adapter yourself but if it's the Mac then only Apple can fix that.

Not much troubleshooting to do. You either don't have power to the AC adapter or the AC adapter is broken or the Mac is broken. It is one of those 3 things.