But I know that there were several Dell models who had this symptom and many people traced it to a stupid design on the plastic casing such that there's a little plastic tab positioned directed above a component such that any pressure on the case eventually wears down the tiny solder connections of the component. Supposedly a careful heating of the solder of the tiny chip solves the problem.
Oh, just googled and there's a wiki entry about this. I have no idea if this would apply to your model. But knowing Dell...
Motherboard
On a number of Inspiron 5150, and 100L machines, a design flaw in the positioning of a tab on the C panel on the underside of the laptop has led to problems. Any pressure applied to the top left hand corner of the laptop causes this tab to press against the motherboard and in particular against the "LVC14A" chip. This causes the solder between this chip and the motherboard to break. This causes sudden shut-downs of the system as a result of any movement of the laptop; in certain cases the laptop will not re-boot at all. Dell has redesigned later models of the 5150 to avoid this problem. Some models reveal cases where someone has manually snapped off the tab from the C panel by hand during the manufacturing process. Dell currently covers this fault in the USA under the Lundell Settlement, although it remains unknown whether Dell will fix this fault for free outside of the USA. As of January 2007 a similar lawsuit started in Canada, and Dell in the Netherlands has agreed to repair Dutch computers following criticism in the consumer programme Kassa<10>.
This has also been a problem with the Inspiron 1150, with the same chip giving problems with broken solder. Re-soldering is not recommended, but re-heating the pins can re-establish the connection and solve the power-off problem - at the expense of possibly losing the use of the touch-pad mouse.
The 5160 has also experienced mainboard failures resulting in an inability to charge the battery or run from the external power supply. Perhaps in response to the previous lawsuits, Dell has been replacing mainboards on these failed units well after warranty expiration, even if the 5160 has been a refurbished machine or resold. Owners must register their current ownership online at the Dell support site, then contact a support representative for service.
This photo shows the chip I'm talking about. I've forgotten exactly which "door" it's under, but if you open them, see if this looks familiar. OTOH, the mobo in yours might be completely different.
http://en.wikipedia.org/wiki/Dell_Inspiron#Battery_recall_of_2006