Yes, that end-cap in the first photo does indeed look a bit corroded, but if that's cleaned off, it should still be fine. There still seems to be some gunk between those two capacitors, though.
Last photo - reflow that solder joint, no big deal. And if that resistor (yes, that's a resistor, not a capacitor) WERE to have reasons to blow, i'm pretty sure that tiny trace coming off that "suspicious" end would've vaporized long before the resistor got toasted.
But if that tablet "took a bath", your problem's definitely not in that area.
One first step would be to switch your multimeter to diode-test mode, red probe on ground, black probe on the positive contacts of the battery connector on the mainboard. Normally that should be 0.6v or thereabouts.
If that's the reading you get, plug the battery back in, and a USB cable into the tablet, and probe the voltage between the red and black wires of the battery.
If nothing happens, you might need to "wake up" the battery externally, with a dedicated charger. Just look for "TP4056" on eBay (local to you, if possible), there should be plenty of those little blue charger boards for just a couple bucks.