I will type in simple English so you understand what I say!
DS needs all parts plugged in to turn on, because it has a built in test when you turn it on that checks for parts. Is a way for Nintendo to make money by not letting you use broken DS at all!
Someone here named TysonDS has made a mod to let you use only bottom, but it is very hard to solder, with small connections.

But, new screens and cases are very cheap for DS from this site, with free worldwide shipping! Here are links to internet pages where you can order a new top screen and a new case:
Screen:
http://www.dealextreme.com/details.dx/sku.3161" onclick="window.open(this.href);return false;
Case:
http://www.dealextreme.com/details.dx/sku.14103" onclick="window.open(this.href);return false;
Those are for DS Lite, if you need original "phat" DS parts, tell me, and I can find those parts for you, too.
To take apart, you will need special Nintendo Tri-wing screwdriver, get here:
http://www.dealextreme.com/details.dx/sku.2905" onclick="window.open(this.href);return false;
Let me know if that helps!