I would be shocked if the cap you have replaced had anything to do directly with your problem. The cap is part of the input side of the voltage regulators and unlikely to directly impact the drivers. What you have experienced is likely the result of physical manipulation of the board during the repair and installation process.
The failure you are describing is likely because the safety circuit in the CCFL driver is kicking in. It either thinks that one or more of the bulbs is not present or that they are drawing too much current.
Looking at the pictures, this looks like a really crude CCFL driver. The two rectangular black blocks with yellow sides are transformers, quite likely set up as Royer transformers. Each transformer drives two bulbs. The bank of diodes in between them near the edge of the board looks for the maximum voltage and trips the safety circuit if the voltage stays too high for too long.
On the back side of the board in this area, there is an 8 pin black chip, which is likely an op-amp, comparator or ASIC that does the comparison. Are there any components in that area that look damaged? Do any of the small glass diodes look damaged? Are the sense resistors next to the transformers OK? Is any pin not soldered down well?
Lastly, one really dumb question. Have you looked at the bulbs and made sure that all 4 light up? Since the safety circuits are all tied together, if one bulb fails, the whole circuit will shut down, even though the other 3 bulbs are functioning properly.
Working with circuits like this can be frustrating when you do not have the schematics or the tools to actually dig into it and find the problem. If I had the schematics and the required tools along with this board in front of me, I would have likely diagnosed and fixed the problem in less time than it took for me to read this thread and post this message.
---55p