Not including cables you have the lid switch, inverter and motherboard.
I'd start with the cheapest part first.
In total there are only about 18 major parts (not including cables, screws, nuts and plastics) so when you get into laptop repair you know what these parts are and to approach repair in two ways. 1. the part you know failed and 2 the cheapest part first.
I just replaced my screen on my dell XPS 1530 and the back light comes on but thats it the laptop starts up ok and I have checked the connections 5 times. What else can I try?