As a suggestion, why not try and find each of the power rails mentioned on page 4, and do a ohms test on them. I'm sure one with a hard short would stand out. Then you can look at what's on that rail, and check all the caps on the rail. It seems to be common for caps to die, even surface mount ones.
But the first step is to find the dead rail. It could be confirmed with measuring the voltage too while trying to power on. The non dead rails will try and lift the voltage, the shorted rail won't, unless its a chip that's away, and not a cap.