I know it's been a long time since I have updated this. But I have made some progress.
Insted of building a proper negative supply circuit with some nice inverting boost converters from Linear I have just used a rectifier to get the voltage inverted. Using my 2ch bench psu I was able to provide the 5V for the logic and the -22 for the LCD line drivers.
See the attachments for the result. I have got all the pixels working but there is no sign of logic as they are all on. I have tried to remove the 5V line and switch it back on, nothing changed. I have checked there is 5V on every IC, I have connected the lid switch as well. I might try just to run the display separately and clock some data into it directly. (I would appreciate some help with this part.)
The backlight is still something I have got to get working. I have tried to trace this part of the PCB back to a schematic so it might help get things worked out. The blue text indicated the connectors between the different PCBs. (attachment #2)
I would really like to finish hacking this now.