Macbook won't take charge from the charger it came with. But WILL take a charge from older generation chargers.

Question

My Macbook will only charge from an older model charger.  The charger that came with the laptop, after the computer overheated dramatically, is suddenly not working.  The weird thing is, the Apple store tried several chargers out just now, including a brand new one, and what we discovered is that the older model chargers work fine, but the newer model chargers (which used to work perfectly) are indeed recognized by the Macbook (there is a little plug/'charging' symbol in the top right) but there is also a message next to the symbol, in parenthesis, stating that the Macbook is "Not Charging".  Any idea what this could mean?  The Apple store said the computer passed all of their rigorous tests... but obviously something is wrong... so they gave me two options: they could either replace the Magsafe unit ($50), or they could send the computer to the "Depot" to have any parts that are malfunctioning changed at one flat fee ($280).  What do I do?  Because I don't want to pay $280 for a new Magsafe unit when I can get it for $50.  But if this is a logic board problem, then obviously I should send it in to the Depot-- but what if they run more tests and decide the logic board is fine?  Any advice would be greatly appreciated.  Thanks.

Answer 1

my ginger,
I did the shift-control-option + power SMU reset.  (My Macbook has an internal battery so I couldn't remove it.)  Nothing changed as a result of that though. 
I checked to see if the battery and adapter are being recognized.  This is what it said (cut-and-pasted below).  Let me know what you think. 
I wonder if the wattage difference in the adapters is what is making the difference... And if so, what that might mean in terms of damage done.  Hmmm. 
Thanks again for your help.  Much appreciated.
Battery Information:
  Model Information:
  Serial Number:          W0952KWJU9X7A
  Manufacturer:          SMP
  Device name:          bq20z451
  Pack Lot Code:          0000
  PCB Lot Code:          0000
  Firmware Version:          0103
  Hardware Revision:          000a
  Cell Revision:          0130
  Charge Information:
  Charge remaining (mAh):          3760
  Fully charged:          No
  Charging:          No
  Full charge capacity (mAh):          4684
  Health Information:
  Cycle count:          442
  Condition:          Normal
  Battery Installed:          Yes
  Amperage (mA):          126
  Voltage (mV):          12054
System Power Settings:
  AC Power:
  System Sleep Timer (Minutes):          10
  Disk Sleep Timer (Minutes):          0
  Display Sleep Timer (Minutes):          10
  Wake On AC Change:          No
  Wake On Clamshell Open:          Yes
  Wake On LAN:          Yes
  Current Power Source:          Yes
  Display Sleep Uses Dim:          Yes
  Battery Power:
  System Sleep Timer (Minutes):          10
  Disk Sleep Timer (Minutes):          0
  Display Sleep Timer (Minutes):          2
  Wake On AC Change:          No
  Wake On Clamshell Open:          Yes
  Display Sleep Uses Dim:          Yes
  Reduce Brightness:          Yes
Hardware Configuration:
  UPS Installed:          No
AC Charger Information:
  Connected:          Yes
  ID:          0x0000
  Wattage (W):          0
  Revision:          0x0000
  Family:          0x0000
  Serial Number:          0x00000000
  Charging:          No