How can I diagnose what's still broken in a water-damaged iPad?

I'm working on a water-damaged 1st generation iPad as a skill exercise, and its current state is that it won't boot up at all, isn't detected by computers, and won't charge when plugged into the wall.

I purchased the iFixit toolkit to take it apart, and I've already soaked the logic board in isopropyl alcohol 3 times, scrubbed gently, and removed all signs of corrosion from the logic board and connectors. I did notice what looked like a bit of corrosion on the bottom-left side of the display panel (when looked at from the front of the device) where there doesn't appear to be any circuitry, just the shielding. Other than that, everything looks to be in good shape now from a visual standpoint.

I have a multimeter but admittedly don't know much about how to properly use it. I did manage to confirm that the batteries seem to have juice at 3.75V, so I don't believe there are any problems there.

At this point, what are my options to diagnose which component is bad? I don't want to buy a bunch of parts since I already have a new tablet to replace this one's functionality. But, I'd like to figure out what's wrong with this one and attempt to fix it. Is there a sure-fire way to say, "Yep, it's the logic board!", or "The digitizer is bad!" without having a bunch of spare parts on-hand to swap in and out?

Thanks in advance.