Thanks Knc1!
I've ordered another Voyage which is in working condition but i can experiment on it february 8th week.
Then i'll open it up, make a backup and use it to recover this one

And i can check if the display is really working (replacing the motherboards).
My toughts about the backup procedure:
1. Take the working Voyage and do a factory restore from the GUI.
2. After reboot, backup the following partitions with a Linux machine:
diags_kernel: diags_kernel.img
kernel: main_kernel.img
system: mmcblk0p1.img
diags: mmcblk0p2.img
3. Flash the backup images with fastboot to the faulty Kindle.
Is there a manual how to backup these images?
Can i still use Geekmaster's getkernels script to get the main_kernel and diags_kernel?
And what about mmcblk0p1 and mmcblk0p2?