Did you ever sort this out? I have a White MacBook with the same problem. backlight comes on, but goes off after a while....

Here is a table of the boards. Linked to some are photos of the boards. http://www.cmizapper.com/board/imac/inde...

This most likely cause by a dead AMD GPU. As this Mac also has an internal (Intel) GPU some things might work just fine. Running the ASD EFI version will usually claim all is fine. The ASD OS version on the other hand will usually crash during boot. As the problems in the dead GPUs are caused by connections coming loose between the silicon die and the carrier that the die is mounted on, and there are very many of those connections, there are also very many different symptoms of having a dead GPU. 1) The most obvious, and tell tale, is when there are coloured lines or coloured blocks or bars in the image on the screen. As the GPU drives the screen even a non-technical user will understand the problem is the GPU. There are more symptoms however that are more devious, and are nevertheless still caused by the GPU... 2) During booting the Mac freezes with the progress bar stuck about half way. This is the point where the OS switches control to the external GPU. Sometimes the Mac will actually still be running...