It's hard to tell, with my limited knowledge. It appears to go through some power supply circuitry that splits it out into separate rails such as 3v and 5v and whatnot, and those go directly into some of the bigger chips on the board.

The fact that the unit seems to partially power up, but it won't do anything with its "logic" such as doing a power-on-reset-test, indicates to me that one of those power supply rails is fried, or as you're suspecting, one of the ASICS is fried.

Fried in a way that isn't detectable by eye, of course. I can't see anything obviously blown on the board.