It's quite possible that when she "ripped" the battery out she may have shorted the leads and damaged the circuitry that recognizes the battery as a source of power. From what you've described the battery is potentially fully charged, or at worst perhaps 90%, so that's obviously not the problem. The USB cable supplies power to the phone in two different ways, as you've discovered.
1) The standard method of power through the USB port is to send charging current to the charging circuitry. The charging circuitry is essentially a completely separate custom purpose computer. It's not dependent on the phone's computer, and its entire purpose is;
- to monitor the battery's health,
- State of Charge levels,
- decide when and if to charge,
- regulate the amount of current going to it while charging,
- allow power to pass from the battery through to the phone,
- or remain off and run on battery power only.
Since the charging circuitry controls all power to and from the battery (and to the phone), it's critical to the phone's ability to boot. If it decides to run on battery power only, or while charging allows power to go TO the battery to charge, power over and above what the battery draws (if charging), is routed to the phone for powering the phone itself. If the battery is damaged, or if the circuitry that charges the battery is damaged, the phone won't receive power since the charging circuitry won't allow it to pass through.
So if the battery is good, as it appears, and if it has even a partial charge, and yet the phone won't boot with the battery connected to the two terminals properly, then this points to a charging circuity failure. Since all batteries are shipped with a charge of approximately 40% to preserve their ability to be charged and prevent self-discharge to zero and shut down permanently, we know that the battery had at least enough power to boot the phone successfully right from the package.
2) The alternate USB power method using a Factory Programming Cable (which supplies power directly to pin 4 as you learned), bypasses the charging circuitry altogether and sends power directly to the phone. If a battery is present and in good health, the Factory Programming Cable will also send a small residual amount of current to the battery - a trickle charge, so this is why it's useful to revive a deeply discharged battery. This is why the phone will boot and operate normally while on that cable, even if there is no battery, but will shut down immediately if removed - even if there's a battery present but the charging circuitry or battery are not functioning normally. This is also why the phone doesn't go into the Charge Only mode when connected to the Factory Programming Cable, since it doesn't send ANY power to the charging circuitry.
I hope that this explanation is helpful in your troubleshooting, and I hope I've given you some information that can help you to further test my theory and possibly isolate the problem. Finally, I hope I'm wrong and there's a simpler explanation for your troubles that won't end badly, but I suspect the damage is done, as they say.