1) Check the AC adapter. Use a multimeter set to DC Voltage, (Symbol is a dotted line over a solid line)
You aren't checking for voltage output, so much, as you are checking for an intermittent break.
AC adapter plugged into power, and probe leads of the multimeter touching the plug of the AC adapter going to the laptop, have an assistant gently wiggle;
1) First the power cord going to the AC adapter.
2) Then the cable from the AC adapter TO the laptop.
If you get an intermittent reading on the multimeter, you have a broken wire in the AC adapter cable, or power cord.
2) If the AC adapter shows VERY close, to the voltage it's supposed to be putting out, AND there is no intermittent break, go to the DC Power Jack.
[ A economical multimeter can be purchased for around $8 to $12.
Available in a multitude of stores. An auto parts store is but one example.
Analog, (Meter with needle), or digital is fine.
Multimeter's vary in style.
It will have a Function knob in the center. This is turned to DC Voltage.
As stated, if just a symbol, it is a dotted line over a solid line.
IF, there is more than one DC Voltage scale, set it to the 0 - 50 Volt scale.
The red probe lead is the Positive lead.
The black probe lead is the Negative probe lead.
You are testing DC Voltage. There is a Positive, and a Negative.
The plug of the AC adapter, that plugs into the DC Power Jack on the laptop, will have a Positive connection, and a Negative connection.
Plugs vary. The most common is a plug with a center hole, and a surrounding metal cylindrical shell.
The Center hole is Positive.
The outer cylindrical metal shell is Negative.
Need more advice post in a Comment ]
Depending on what laptop we are discussing here, the DC Power Jack can be soldered directly to the motherboard, OR it has a cable attached to it, and the cable plugs into the motherboard.
(DC Power Harness)
IF, it is the solder to the motherboard type, it has prongs, or pins, that come out of the bottom of the DC Power Jack, and goes through the motherboard. Then the prongs, or pins, are soldered to the motherboard.
With this style, if the DC Power Jack is bumped, the solder joints of those pins, may be cracked. Makes a bad contact.
Could also be bad enough to make a Short. (Laptop turns off when AC adapter is plugged in)
The DC Power Jack itself may be in bad repair.
Using as an example of the style that has a Center hole, and a surrounding cylindrical metal shell, (Inside), if the two parts touch, you can have a Short.
The diagnoses is to start with removing ALL power, AC adapter ('Natch), and Battery.
See with a small wooden object, if you can gently wiggle the DC Power Jack.
ANY perceptible movement means a bad DC Power Jack.
You will also have to partially disassemble the laptop, to check the DC Power Jack solder connections, to the motherboard.
3) DC Power Jack checks out, the problem has gone serious.
Mounted to the laptop motherboard is a power controller chipset.
It is a power MOSFET,
[ Chip and Chipset are slang terms for I.C.
The power MOSFET is a type of I.C.,http://en.wikipedia.org/wiki/Power_MOSFET
If you open the laptop, and view the motherboard, this problem will be readily apparent. This chipset usually burns, and turns blackish.
Problem is when it does, the manufacturer's ID numbers are hard to read, in order to obtain a replacement ]
This is one power controller chipset that is used in a LOT of laptops,https://docs.google.com/viewer?a=v&q=cache:oER5NNz8cwcJ:www.fairchildsemi.com/ds/FD/FDS6675BZ.pdf+Fairchild+FDS6675BZ&hl=en&pid=bl&srcid=ADGEEShOhWPjm_M-ROHme4iEMrztCTOd-28jNiy1hVLQQh_VOyv8zcXEVDB_iTQA6MuZO88UmRkDgjyW9j4CP2aIJ-4DS-h6JNM3lvxldeApQeecmz_DADCw1s7tmNLxfPknqX14SZP6&sig=AHIEtbS_rYUAeo_8rB9YHkW05ZjLqeH4Jg
This is another one,http://html.alldatasheet.com/html-pdf/85156/VISHAY/SI4925BDY/183/1/SI4925BDY.html
Both of these chipsets uses a D2PAK surface mount.
The leads are bent into a J shape. ( J Lead)
The 'foot' of the J lead is soldered to a copper pad on the motherboard.
(Copper Pad has a thin gold plating on it)
Simple de-soldering/soldering techniques, are used to Remove the chipset.
HOWEVER, use a Heatsink on EACH J lead, when soldering the new chipset in.http://www.radioshack.com/product/index.jsp?productId=2103242
(The power MOSFET has transistor/s inside )
OR, replace the motherboard.
For additional questions please post in a Comment.