Video chip fried up. how to get it replaced?

I don't know where you could get this part. they are not like on other devices - sony used a "graphics synthesizer" on the ps2. and they had not only one kind of it.

what happend to your graphics synthesizer ?

does the ps2 show any kind of "video" signal or is it completely dead ?

maybe the chip could be resoldered/reflowed (or reballed)

i don't know if someone in your area does this and how much something would cost. here in germany almost nobody would do that - a brand new ps2 costs sometimes around 77€ - a repair like that would be in the same pricerange