Is this a picture of your device or just a picture you found on the web? Have you tested the individual components in the backlight circuit?
I would start by validating that L2200 is in good condition. Then check the diode to insure it is working properly, even if you replaced it. You may have damaged it with too much heat while soldering it. I wold also check the coil. If needed, you may need to replace all of those components plus the driver IC.