How does one distinguish a dead battery from a dead logic board?

I recently purchased some soldering equipment with the intention of repairing iPod Touch batteries, but I must know one thing before I continue this endeavour.

If an iPod touch does not turn on at all, how does one know if it's simply the battery that is at fault, versus the logic board being shorted out or something similar? I wish to only replace batteries on units that would benefit from it, obviously.