Definately sounds like your battery has had it!
You should find a new one here http://www.portableparts.co.uk/partsr/Dell_Latitude/38
i have a hp pavillion dv8000 and i have some weird charging problems. At first i had to jiggle the little plug that goes into the laptop in order for it to start charging...I figured thats probably because the cable had some wires that were not connecting pretty good so i bought a new charger with the same voltage. Now i get a diff problem. I plug it in and it would work fine for about a minute then the lamp that shows the power and charging starts to flicker....i plug it in and out again and same thing...sometimes it works but most of the time i get really frustrated with it...I tried sending it for repairs and they said its "fixed" but obviously its not....I really hope someone can help me out on this one since i am really desperate...is it maybe the charger again or something inside the laptop that overheats and stops working...i have no clue honestly...but i hope you guys can help out.
thanks a lot