If you have your original OS X disks, or the program TechTool Deluxe or TechTool Pro, you can test the hardware to see if there are any obvious hardware issues. Insert the original OS X disk that says 'AHT Version x.x' in small print on the label, and reboot holding the alt key down. Assuming that works, choose the Apple hardware test, and when prompted choose the extended test. Does that tell you anything?
When you say the screen doesn't turn on, if you shine a flashlight at the screen, can you see writing or graphics on it?