I have replaced the screen (+digitizer in a whole) and since then it is randomly going off and on. Interestingly it even did the same in recovery (TWRP 2.3) BUT not with every software! Installing the TWRP 2.6 or above stopped it happening in the recovery.
I have tried various ROMs so far. The Eclipse ver3 did not flicker, but it has a problem with the registering on a network here in the UK. Stock + stock based ROM (Rage 1.2) are also switching on-off. I am currently looking for a working ROM.
Please let me know if someone with the same problem can find one.
Also tried to play with developer options like Disable HW overlays or Force GPU rendering with no effect.
I wonder if it is a different hardware version of the replacement screen or what else can it be? (screen came from etradesupply)