Could be a combination of things.
1) Battery is low. Not enough power to turn the laptop on.
2) AC adapter has a plug on the end of the cable. The plug plugs into a DC Power Jack on the laptop.
The DC Power Jack is bad.
2a) The DC Power Jack has a bad connection to the motherboard, (Cracked solder joints), and/or the jack itself is bad.
2b) Center Pin is loose in the jack's mount.
The back of the Center Pin where it mounts has become loose.
2c) The plastic body of the jack, which composes the jack's case, is cracked. This allows movement of the Center Pin.
2b, and 2c cause a bad connection with the AC adapter plug.
No charge to the Battery, no power to the laptop.http://www.laptopjacks.com/view_part/For-Gateway-MX6920-DC-Power-Jack-GW51425.html
[ If this is the case the DC Power Jack needs to be resoldered to the motherboard. The cracked solder joints need to be re-melted, (Reflowed)
Entire laptop needs to be disassembled down to the bare motherboard in your hand.
(No Processor, Ram Memory, or any adapter cards mounted to the motherboard. Nada)
The DC Power jack needs to be replaced.
This entails disassembling the entire laptop, down to just the motherboard in your hand. (Same as above)
The old DC Power Jack is de-soldered, and a new one soldered in place.
Very FEW computer repair shops have the necessary skill level.
They just want to replace the entire motherboard.
IF one is available.
More Ka-Ching for them also. ]
3) The AC adapter is bad.
Not providing power to the laptop, to charge the Battery, nor give power to the laptop without the Battery.
AC adapter cord from adapter to plug, which plugs into the laptop, (DC Power Jack), may have a break in it.
May be an intermittent contact provided by wiggling the cord.
If this is the case the wires have stretched, and broken.
Wiggling causes the wires to briefly touch, and make contact.
Where this cord meets the plug itself. A lot of times there is a break in the wires in this area.
Solution is to replace the AC adapter. There are universal AC adapters you can buy, or perhaps Gateway still has some for sale.