Yes, there does seem to be something odd going on because one of the combinations of connections should work OK on most TVs (as far as I know).
My thoughts are that:
(1) there is a specific fault with the system somewhere: jack socket on TV, or phono to jack cable (the PS2 to phono lead has been proved because it works when plugged in the back of the TV).
(2) the TV has a non-standard A/V jack socket arrangement (knowing the TV model may allow this to be resolved)
(3) the output from the PS2 needs to be set up from the configuration menu
(4) the output from the PS2 needs to be set up from the configuration menu
(5) the jack plug is simply not going fully home into the jack socket on the TV for some mechanical reason
This seems to be the most common TRRS (Tip Ring Ring Screen) jack plug audio visual pin out (composite video, individual left and right audio, ground [screen]:
My thoughts are that:
(1) there is a specific fault with the system somewhere: jack socket on TV, or phono to jack cable (the PS2 to phono lead has been proved because it works when plugged in the back of the TV).
(2) the TV has a non-standard A/V jack socket arrangement (knowing the TV model may allow this to be resolved)
(3) the output from the PS2 needs to be set up from the configuration menu
(4) the output from the PS2 needs to be set up from the configuration menu
(5) the jack plug is simply not going fully home into the jack socket on the TV for some mechanical reason
This seems to be the most common TRRS (Tip Ring Ring Screen) jack plug audio visual pin out (composite video, individual left and right audio, ground [screen]: