By "just died" do you mean that it will not respond when you press the power button to start up?
If that is the case, your first step should be to reset the system management controller. Use the steps in this Apple article.
Note that your battery may need replacing soon. Is it original with the MacBook?
Best of luck.
You can get a new third party battery fairly cheap on eBay. Every MacBook from 2006 through Mid 2009 except the Late 2008 Aluminum Unibody and the Late 2009 and 2010 White Unibodies use the same A1185 battery.
Or for $129 from The Apple Store http://store.apple.com/us/product/MA566LL/A?mco=MTY3ODQ5OTY