Hi, I have the same black Macbook (bought at the end of 2007) and the same problem.
It started about a year ago. I tried to find information about the problem here, but all I found was related to the inverter cable and some people said that it does not fix the problem permanently for them.
The fan thing is also happening to me, I noticed that when the problem with the screen started, the fan also started to speed up more.
I'm using the Macbook as second computer, so the problem doesn't bother me that much.
When it happens, something that temporary fixes it, is to set the brightness to zero (with F1) and the increasing it slowly.
It also helped to set one of the active screen corners as "Put Display to Sleep". When you get a black screen you activate that corner and then move the cursor to awake the display and the screen comes back.
I've try reseting the PRAM, removed the battery, etc. but nothing fixes it permanently.
Please let me know if you find a solution!