After that I tried the old screen without a backlight and it still had the same problems.

(PS: Sorry for my bad english)

sounds like the screen is fucked ))

It's quite an interesting observation. I haven't considered that...

Bad ribbon cable connections?

I don think it's a problem, cable looks fine, connection also looks all right... It worked fine until some moment, I can't recall that I have changed anything since then...

What mods have you done to it other than the backlight, what backlight did you use, and did you use a resistor?
The only things I can think of that cause that to happen is if you're using a variable clock and you've got it slowed down, or if you're not getting enough power (batteries can be ruled out since you said it works fine with a different screen, so it could possibly be related to the backlight).

Sorry I forgot to mention. When I desolder backlight wires fizzling is still there, it doesn't fix the problem.

Variable clock is off, however it is indeed resembles underclocked 'shaking', but sound is fine and another screen works flawlessly. This also rules out lack of power.

Also capacitors seem to be fine, nothing blown.

I was modding a DMG and suddenly the image on the screen started fizzling (impossible to capture on camera). There are basically there are thin horizontal lines blinking very fast as in the old badly tuned TV set. So you basically see the picture but it's soft of shaking. When I try another screen there is no such problem.

The screen is backlit and it worked fine until recently. Of course there's always a chance I accidentally damaged something and didn't notice but if you know the exact reason please share

Thanks!