BQ77PL900 Fails to Startup

The part certainly sounds off. From the description it would seem to be in the "UVLO mode" block of the figure 3 flowchart waiting for the regulator voltage to come up.
1. I don't recall this type effect, but there could be something here on e2e or some other history which I don't know.
2. ESD can cause various failures in electronics, sometimes developing over time. Failures are not necessarily consistent from part to part.
3a. Yes, the regulators should come up, but voltages may not be as stable as the specification.
3b. Corrupt configuration may be possible, but should not be the cause of the regulator not starting. Without logic voltage the configuration would not be used.
4. In general: check voltages, component values and solder joints: be sure to check the voltage at the device pins. Check to see if currents vary as you adjust available input voltages (PACK+ voltage here). Analysis techniques will vary. Comparison to a working system is often helpful. At some point you may need to remove the IC to test other circuit components or subsets. Determining if a new IC fixes the system can be helpful as well as if the removed IC passes test or operates in another system. The IC could be sent to a lab for test or failure analysis.
5. The charge pump will always be active, either in bypass mode or voltage division mode. See the block diagram on page 6 of the datasheet. Note that the part can get power from either the BAT pin or the PACK pin. (But it is the PACK pin which has the wakeup circuit). Note also that the regulators operate from the CPOUT pin. CPOUT should be either approximately the higher of the BAT or PACK pin, or half that. With the part in shutdown the charge pump should not be active and CPOUT should be high, you should be able to see it move with the PACK voltage if you manipulate it, but without operation and a large capacitor, the voltage may be slow to fall. If the charge pump is active, and 24V is a point where it may begin to turn on with sufficient load, CPOUT should be about half the higher of BAT or PACK. If running, the grounded CP capacitor should have approx the same voltage with some noise. One side of the flying capacitor should switch from GND to mid voltage, the other side from mid voltage to BAT or PACK voltage. Switching is in the 10's of kHz, you could observe a working system for comparison if desired although there will be some variation part to part.

Thanks WM5295. Am I right in thinking that when there is less than 3mA out of the Vreg pins that the charge pump is in bypass mode and CPOUT should track the higher of BAT or PACK? Then if the current draw out of Vreg is enough (>3mA) then the charge pump goes into voltage division mode and CPOUT drops to half the higher of BAT or PACK. That would reduce the heating on the Vreg circuits, ya? On the part we're having trouble with, CPOUT languishes around 0.6V even if PACK is 28V and BAT is 23V. So it doesn't appear to be moving with PACK.

Yes, your understanding seems correct, each part will determine the current and voltage at which it needs to start the charge pump voltage division mode. The part sounds like it is broken, questions might be if there are any clues on the board as to what caused it, what it was exposed to, and what is the particular damage.

VI curves are a common analysis technique which can be applied at various levels of a system. I would expect it would be helpful, they often help show opens, shorts or altered behaviors.