I recently bought another gas plasma Toshiba, the 286 T3200. After cleaning internals, taking out the hard drive, doublechecking every element on board and making sure the voltages are right I tried to turn it on.
The computer won't boot properly and here are the symthoms. I'll write down everything what I think can be useful for you.
-The power supply is buzzing with no load (I don't know if it does the buzzing with all components plugged in because fans are too loud) but voltages are perfectly fine and stable
-After pressing power button Toshiba generates long single beep. The screen doesn't glow, only things appearing on the screen are little orange spots under top bezel, just like on my working T5100 when the screen is turned off by closing the lid, so I assume that's okay.
-Sometimes the screen does come on, but after a few seconds it shakes and goes black again. It's a lottery. When it glows contrast and brightness regulation work. The screen itself looks perfect without any damage
-System is halted with "KBC SELF TEST ERROR" message that I can see when image on the screen appears.
-CPU is getting warm after a few minutes, I don't know if it's okay or not.

My conclusions so far:
-Voltages are fine
-There are no capacitors leaking, I can see some brown gunk near one of the smaller electrolytic capacitors on the motherboard, but I assume that's just some kind of dirt, not the electrolyte.
-Gas plasma doesn't glow when only HV connector is attached (205V and 5V) , but I think that's normal because my working T5100's screen doesn't too. Considering that I think that motherboard doesn't send the proper signal to gas plasma.
-Every chip is settled correctly

The most important thing for me right now is to test the gas plasma unit, I want to be sure that it's fine. There are no pinouts for this part on the internet. I have functioning Toshiba T5100 and even though the connections look the same and screen fits in it's housing, I'm not going to test it this way, because they're not exactly the same and I don't want to risk my perfectly fine T5100.
Back to the motherboard I'm absolutely out of ideas. I've just ordered the capacitor tester and I'm going to test every capacitor on the motherboard, is there anything else I can do? I'm thinking about logic probe too.

Here's an example video. Generally the screen lights up for a little bit longer time but less frequently.

I'm waiting for your ideas what's wrong with this machine.