Are any of the missing rails shorted to ground?

I think its OK. I checked 0V mosfes and they seams to be OK.

Maby its something with 6225CA but how to check it?

There's some schematics for NV28 from MSI ms-8894
It's a pity but it has different PWM controllers. But anyway you can understand what voltages should be.

ISL6225 - is for memory and maybe 3.3V
ISL6525 - is for a gfx chip

To work first of all they should get power voltages on their VCC pins, Enable signals are active.
There shouldn't be short circuit in load. The mosfets should get power too.

Thanks for schematics, I will look at it later.
I just checked VCC pins and voltage is present:

6225 - 5V
6525 - 12V