My Gateway laptop, NE56R1u, shuts down automatically when unplugged even though fully charged?

SOURCE: Won't Charge Any Battery--Even a New One

Check for loose solder connection in the power supply and the terminals that connects the battery to computer.

SOURCE: Gateway nv52 won't turn on

I also had this problem. I turned it off and it would not turn on. I found the solution. First, extend the laptop screen as far back as it will go. Don't just stop the screen at a ninety degree angle. My laptop screen pulls back to about 135 degrees. Now press the power button. It should start up.

Why do I think this works? Well...I used to own an older model thinkpad that had a short "male" connector on the screen, that when the screen was folded down would enter into a "female" connector on the base of the unit and trigger sleep mode on the unit. This is how the system could automatically hibernate when the screen was closed. The little male connector broke off, and I couldn't get the system to wake up, because the connection to tell the laptop that I had the screen up or down no longer worked. I couldn't even power it up. I had to take an ink pen and push the connector through the female end to indicate to the motherboard that I'd opened the screen before it would even turn on.

It appears that the same type of mechanism is built into the long BAR under the screen of the NV52 and somehow it can't determine when the screen is open or closed. If it detects that the screen has not been opened, it won't power up. This safeguard prevents the laptop from being turned on mistakenly while closed up in your laptop bag. Extending the screen back resets the mechanism and it should turn on. Sorry for the long explanation...

SOURCE: My Gateway laptop NV54,shuts off when i either

I would suspect a bad connection on the motherboard since you say your battery is OK--I take it to mean that your computer runs when plugged in or on battery.
Try this:
Leave the charger plugged into the computer and unplug it from the wall. Then plug it back in. Do you have the same problem? If not, then it's the physical act of plugging the plug into the machine that is causing the problem and that would be causing some kind of contact problem on the motherboard.

SOURCE: gateway black screen

If your laptop appears to boot up and the hard disk LEDflashes, then the problem is probably a back light fault. This can be a faultyinverter or a faulty CCFL lamp. Please click on this link and follow myinstructions to identify the fault and possible fix :- http://www.fixya.com/support/r3598095-faulty_laptop_lcd_screen

SOURCE: Gateway ID49C07u overheating + battery problem

Get a can of compressed air and clean out all the vents and fans. You can also use a vacuum with a hose attachment to clean it. You also might want to get a laptop cooler.

Also, Facebook is constantly under attack from malware and virus peddlers. You might want to try doing some malware and antivirus scans with some of the FREE software listed below:

Start your PC and press F8 several times until the boot menu comes up. Then select "Safe Mode with Networking". Now get some or ALL of the FREE programs below.

Download, Install and Run Malwarebytes Anti-Malware:
http://majorgeeks.com/download.php?det=5756
When Installing choose the non-pro version.

Download, Unzip, Install and Run TDSSKiller:
http://majorgeeks.com/Kaspersky_TDSSKiller_d6895.html

Download, Install and Run Super Anti-Spyware:
http://majorgeeks.com/SUPERAntiSpyware_d5116.html

If you have an outdated Anti-virus program then Download, Install and Run Avira Anti-Virus:
http://majorgeeks.com/Avira_AntiVir_Personal_-_FREE_Antivirus_d955.html
Make sure to select ALL of the "threat categories" when you install or configure Avira...

You should be in pretty good shape if you run and install all of these programs.