1) Start out by removing all power to the laptop.
Of course you probably have the AC adapter (Charger) removed, but also remove the Battery.
See if you can gently wiggle the Center Post.
Also look to see if it seems that the entire DC Power Jack is moving around.
You may have to scrutinize pretty close to see any perceptible movement.
There should be No perceptible movement at all.
This is an example of a DC Power Jack for an Asus Eee 1005HAB Notebook PC.
It may, or may not, be The DC Power Jack you will need, but is used here for an example of the DC Power Jack construction,http://www.rolta.co.uk/new-asus-1005hab-laptop-power-jack-pin-socket-dc-connector-165mm-29396-p.asp
You can click on any of the three views shown, and have all three views enlarged.
Click to enlarge.
Looking at the view on the far left, the Front view. You will see what appear as three pins sticking up.
These are Prongs.
Shown again in the Back view, which is the middle example.
These two views show the DC Power Jack upside down, in relation to how it sits on the motherboard.
The Prongs go down through holes in copper circuit traces on the top of the motherboard, and are soldered to the motherboard on the bottom side.
A) From accidentally bumping the AC adapter's plug while inserted into the DC Power Jack, the solder joints may have cracked. This can also happen with just normal usage from plugging, and unplugging the AC adapter.
Solution for this is to re-solder the cracked solder joints.
Sounds easy, but in reality the entire laptop has to be disassembled down to the bare motherboard in your hand. No Processor on the motherboard, no Ram Memory, no nada, but the bare motherboard.
Soldering can ruin a Processor, Ram Memory, or associated hardware components still installed on the motherboard.
B) The DC Power Jack may be broken. The Black body of the DC Power Jack that you see in the examples, is made of plastic.
This entails de-soldering the Prongs of the DC Power Jack, removing it, properly cleaning the area, (area around the copper circuit trace holes in the motherboard), re-tinning the area around the circuit trace holes, then installing the new DC Power Jack, and soldering it into place.
This is a basic example of DC Power Jack replacement,http://www.laptoprepair101.com/laptop/2007/12/06/dc-power-jack-repair-guide/
C) The motherboard area that the DC Power Jack is soldered to, can be compared to a 'Peninsula'.
A small strip of motherboard that sticks out away from the main body of the motherboard.
This 'peninsula' can crack at the area where it meets the motherboard.
This will result in stretched broken circuit traces.
[Think of a circuit trace as being a very flat, thin, copper wire ]
If this has occurred toss the motherboard.
[ In regards to the DC Power Jack repair guide in the link above;
1. You don't need a soldering station. A soldering iron around 40 to 50 Watts with a No.2 chisel tip, and well tinned, will work just fine. Have a very damp sponge nearby to constantly clean the tip with.
2. I advise using Desoldering Braid instead of a Desoldering Tool. The braid is laid on the solder joint to be removed. The tip of the soldering iron is laid right on the braid, above the solder to be removed. The copper braid will 'soak up' the solder.
A lot handier than a Desoldering Tool IMHO.
3. Isopropyl Alcohol is EXTREMELY FLAMMABLE! Do not use near the soldering iron, and use in a WELL ventilated area with NO sparks or flames present!
4. If you are rusty with your soldering/de-soldering techniques, practice awhile before attempting this procedure.
Do Not overheat the copper circuit trace area around the holes. This will burn the area, and it won't accept tinning. (Tinning: Applying a light coat of solder) If it will not accept tinning, toss the motherboard at the cat. It's junk.
Overheating can also lift the copper circuit trace right off of the motherboard.
Make SURE you make a pretty, clean, solder joint. A cold solder joint will result in you starting all over.
It's a pain in the keister to disassemble the laptop in order to repair a cold solder joint.
Make sure the soldering iron tip is clean, and well tinned before you start.
Clean the tip often by wiping it across the damp sponge ]
The center pin of your DC Power Jack may be 1.0mm in diameter, or it may be 1.65mm
Make sure you obtain THE correct DC Power Jack.
The one's that are advertised around $2 to $5 may be junk, and no where near the actual DC Power Jack you need.
This place may be the one to go to. Don't know, haven't tried them, and not advertising for them.
I do like how they want you to send a photo in, and they also ask questions BEFORE you purchase.
IMHO it seems as though they may be professionals in their area of expertise,http://www.laptopsockets.co.uk/
If you wish to have a Service Manual I do not see any online links to give you, except for one that details how to disassemble down to the Harddrive.
From there it would be a guide to an Asus Eee PC that is fairly close IMHO.
Plus guidance from me.
Have questions mtrunner53 please post in a Comment.