Can i replace One big transformer with two
The noisy video on the LCD is most likely due to arcing in the CCFL high voltage board but the actual root cause is unclear.

If you are certain the transformer is flawed , a replacement will need exact parametric properties to meet the requirements of the CCFL driver IC.

This would include inductance, turns ratio, HiV rating value, self resonant frequency because this operates with PWM using zero-valley switching to regulate the trigger voltage and sustaining current thru each CCFL within the range of operating frequencies used. There are finely tuned RC delays on board to match these characteristics.

It may be easier to replace the board. 

Phosphor wear and contamination to the CCFL's increase conduction current along with declining brightness and it may be time to replace the tubes as well from Digikey according to length and thickness [mm].

Here are the IC specs.