MacBook "Not Charging" after new power adapter.

Question

Last week the power adapter that came with my 13in MacBook began to melt. I ordered a new adapter "60w MagSafe Power Adapter" plugged it in, and it lit up, but now my battery information on the screen says "Not Charging" and If I unplug the adapter, the computer completely shuts down. I had no problems with the battery or the adapter before the "meltdown" Gosh, My Mac was still charging even while in fire hazard mode Lol! Why is the new MagSafe adapter not charging my MacBook? Please Help!!!
Here's what I am getting under the power information:
Battery Information:
  Model Information:
  Manufacturer:          DP
  Device name:          ASMB016
  Pack Lot Code:          0002
  PCB Lot Code:          0000
  Firmware Version:          102a
  Hardware Revision:          0500
  Cell Revision:          0102
  Charge Information:
  Charge remaining (mAh):          0
  Fully charged:          No
  Charging:          No
  Full charge capacity (mAh):          0
  Health Information:
  Cycle count:          1128
  Condition:          Replace Now
  Battery Installed:          Yes
  Amperage (mA):          0
  Voltage (mV):          9596
System Power Settings:
  AC Power:
  System Sleep Timer (Minutes):          0
  Disk Sleep Timer (Minutes):          10
  Display Sleep Timer (Minutes):          15
  Automatic Restart On Power Loss:          No
  Wake On AC Change:          No
  Wake On Clamshell Open:          Yes
  Wake On LAN:          No
  Current Power Source:          Yes
  Display Sleep Uses Dim:          Yes
  Battery Power:
  System Sleep Timer (Minutes):          15
  Disk Sleep Timer (Minutes):          10
  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:          0x0100
  Wattage (W):          60
  Revision:          0x0000
  Family:          0x00ba
  Serial Number:
  Charging:          No

Answer 1

Hi Marlisa,
#1 Your battery should be replaced if it has actually gone through 1128 cycles. Most batteries don't last near that long.
#2 Reset the SMC