Fnally, a Recent thread on this subject...
There's 2 different power issues on Inspiron 2500/8100/8200 Laptops I have seen.
I have been re-building working machines from about 40-odd dead ones, so I probably have seen almost oll the issues by now.
One is using under-powered chargers (70watts from a 2500/8100) on an 8200, which wants a 90watt charger. The 70watt will charge the batteries on an 8200, but if you run the computer with it the machine will operate using your Battery Mode energy saving settings. Not a catastrophe. Just go into the BIOS setup and set the batter mode settings to all the max settings. Just remember you did that if you DO operate on betteriy, because it will drain faster.
The second is a little harder. Under the palmrest, right behind the touchpad, is the batter charger/power circuit board. The "stud" that this screws into easily breaks free from the motherboard, and the board gets loose. The bext wat to fix it is to take apart the machine, epoxy it back on, and re-assemble. The card has 1 screw and is also held by one of the palm screws that passes thru it. Don't use crazy glue!!! Please. That junk dries-out and falls apart on non-porous materials. Use Epoxy.
You have to remove the keyboard (4 screws) and palmrest (8 screws) AND the display (3 screws) to really get in there. Also the video card is you have one of the accelerator cards like an nVidia (3 screws).
The 3rd screw on the video also uses that same stud, so it MIGHT just spin. If so, pull out the video card, and lift the power board up with it. Hold the stud with pliers to remove the screw.
CAUTION: There SHOULD be a spacer on the Left screw hole of the power/charger board. I looks like the stud, but has no internal threads. It Usually stays stuck to the charger, but not always. So make sure it's not rattling around in the machine. Also don't mix them up... Give the epoxy time to dry before re-assembling.
This is a good time to blow-out the dust on the CPU cooling fins, too...
If it still won't power-up, the motherboard has issues, and it's not worth fixing unless you have free access to parts. Sell it for parts on eBay, or buy another dead one and Frankenstein them together. Like I have been doing...