I was looking more into this - there isn't much specific info on putting out powerful battery fires.
The type C extinguishers are probably fine for electrical fires involving exploded/flaming batteries. The big thing they do is prevent you from being electrically shocked from an energized source.
The type D is very good for chemical and ''exotic'' metal fires because certain chemical/water extinguishers will make the fire worse because the hot metal will react with the chemical/water.
I have heard that a type C carbon dioxide fire extinguisher will also work - it suffocates the fire by blowing away the oxygen with carbon dioxide (which the fire cannot use).
For all extinguishers, you should be fine with being 4-6 feet away from the fire itself. Being too close could be too focused, too far would limit the extinguishment ability.
As soon as I get specific info on fire extinguisher tests done on laptop/battery fires, I'll let you know.
Best,
Shalin
Based on my experience as a volunteer firefighter, I'd like to share some info that doesn't cost and arm or a leg...but may save both in the case your laptop/battery explodes:
Firstly, DON'T USE WATER. duh.
It's best to use a dry chemical extinguisher (type "C") on an electrical fire.
However, use a dry powder type "D" extinguisher for the dense chemical battery (NiMH, Lith-Ion, plain old alkaline, etc.). The type "D" extinguishers are designed for chemical and combustible metal fires (e.g. magnesium fires with some automobile engines). You should be able to use the "D" type extinguisher to put out electrical fires as well.
It may seem like an odd idea, but dumping sand on a chemical fire also will work to an extent. This is just a simple smothering technique. Kudos if you actually have sand nearby...
Below are a few informative websites on battery fire safety and fire extinguishers:
http://www.fireextinguisher.com/
http://www.fire-extinguisher101.com/
Energizer Lith-Ion battery material data sheet: http://www.ntsb.gov/events/2006/PhiladelphiaPA/Exhibits/350561.pdf
Woods Hole Oceanographic Institution study:
http://ehs.whoi.edu/ehs/occsafety/LithiumBatterySafetyGuideSG10.pdf
*****Other related information*****
Lithium Ion battery in cars: http://www.digg.com/tech_news/Lithium_Ion
Technology Review - Lithium Ion cars: http://www.technologyreview.com/read_article.aspx?id=17250&ch=biztech
NTSB study: http://www.ntsb.gov/events/2006/PhiladelphiaPA/Exhibits/350561.pdf

Chowhound
Comic Vine
GameFAQs
GameSpot
Giant Bomb
TechRepublic