We've been having problems with our Dell Insprion 8200 recently...  mainly to do with the power supply and connector.  For a while there, it could be fixed by pushing the connector a certain way or propping something underneath the laptop.  As it turns out, we were experiencing two problems at once and just didn't realize it.  The first was that the cord on the power supply near the laptop connector had worn to the point that the smaller wires within the big wire had broken.  I had to cut this open and manage to solder them together.  I should probably purchase another power supply since this is likely to happen again since it has already happened to the three power supplies I already had.  The second problem is that the connector on the motherboard the power cord connects to was flakey.  Do you see the four regularly-spaced solder joints?  On the bottom line of that rectangle, do you see the triangle shaped set of three?  The connection on the bottom left corner is a bad solder joint.  I have no way of knowing if this came from the factory this way, but it's for sure there now.

I did fix it for a while by re-soldering the pin of the connector back down (effectively repairing the existing joint), but that eventually wore out again and I finally ended up soldering a wire to the back of the power connector and soldering the other end of it to the chip you see in the bottom right here, effectively bypassing the trace on the board.  The laptop seems to be fine now, it just looks a little strange to see an extra wire in a laptop.