Inside? Yes. (If 'charger' is good)
A) AC adapter (Charger), has to be KNOWN to be good, before going on.
Used on a working laptop to see, or multimeter is used to check Voltage (DC)
The plug end that goes to the laptop, from the AC adapter, has a Center Hole, and a cylindrical outside metal shell.
The Function knob is set to DC Voltage. If just a symbol, the symbol is a dotted line over a solid line.
If more than one DC Voltage scale, the Function knob is set to the 0-50 Volt DC scale.
The Positive (Red) probe lead of the multimeter goes to the Center Hole, and the Negative (Black) probe lead of the multimeter, goes to the cylindrical outside metal shell.
You should be reading 19 Volts DC.
Also have an assistant gently wiggle the cable FROM AC adapter TO laptop, and the power cable TO AC adapter.
If there is a fluctuation on the reading, there is a broken wire, or wires, in one of those cables.
B) Check the DC Power Jack.
This is the jack on the laptop (DC_IN) that the AC adapter plugs into.
Has a Center Pin, and an inner cylindrical metal shell.
Battery removed, use an eraser on the end of a No.2 pencil, and see if you can GENTLY wiggle the Center Pin around.
ANY perceptible movement of the CENTER PIN, means replacing the DC Power Jack,
(By the way, is it an 8510p, or 8510w?)http://www.alldcjacks.com/en/ppj052-laptop-dc-power-jack.html
Any movement of the rest of the DC Power Jack (Body), means replacing it; or may just mean the solder joints are cracked, and can be re-soldered.
C) AC adapter and DC Power Jack checks out?
Problem may be with Power MOSFET's on the motherboard, and associated MLCC's.
(Multi-Layer Ceramic Capacitor, and they are SMD/SMT just like the Power MOSFET's.
Surface Mount Device/ Surface Mount Technology)
Using HP pavilion dv6000 series, and Pavilion dv9000 series Notebook PC's, for an example,http://mayohardware.blogspot.com/2010/04/important-parts-on-dv6000-and-dv9000.html
Or, it could be worse,http://koti.kapsi.fi/jpa/stuff/pix/travelmate_6292/