i replaced a top screen recently, it is possible that the cable may be damaged, i know that if the cable is loose then the bottom screen flashes white and turns off.

http://www.youtube.com/watch?v=fw4FJYWFwbg

this is the video i used to learn to take it apart, be aware you will need a triwing and a phillips screwdriver to open it up and will technically void your warranty but there is no real way nintendo can tell if you open up a ds lite.

if the cable is loose then it is a very easy job, push the cable back in, push it in as far as it will go (i made this mistake first time, cable was not pushed in all the way in even tho it was held by the clip)

if the cable is damaged or you need to replace the top screen then its a harder job but doable, the hardest part is rolling the cable into a tube and threading it through the hinge.

if the top lcd needs replacing then you will need a soldering iron to transfer the speakers to the new screen (i did this with a normal iron but a fine tipped one wouldve been much easier)

the housing may need replacing but you could consider removing the housing and then fixing it with superglue. hope this helps

all the parts and tools required are readily available on ebay, even the screen was only £2.50 from china, was a little darker but works perfectly