Kansas19,
As I stated, the E4 battery pack is the standard 'dumb' type, without any gas guage battery mangement within (unlike laptop batteries that use BQxxxx chips. The components that you can see are, as others have stated, related to the mandatory Li-Ion technology safety systems to prevent overcharge and discharge. As you likely know, Li-Ion cells have a habit of exploding and/or catching fire if abused during charge or discharge. The Power MOSFETS cut the charge or discharge path if the safety monitoring chip detects an excursion outrside acceptable parameters.
This includes an overdischarged or faulty cell A Li-Ion cell must not be overdischarged. Doing so permanently changes its internal chemistry and can lead to unstable/unsafe operation in extreme cases. The safety chip measures the cell voltage, and if it drops below a set threshold, it disconnects the cell from the outside world using the MOSFETS, both charge and discharge are prevented.
Unlike many laptop batteries that are 'intelligent', the safety chip does not normally do a non user reversible 'lock-out'. (With BQ chips, that are password protected, you can unlock them but the software is expensive and you need the password). It is often possible to recover an overdischarged Li-Ion cell with sort charging pulses until the cell voltage rises to the safety threshiold, the cell input and output MOSFETS are then reactivated for a normal charge process. The cell recovery process can take many forms, one of which is to open the plastic cell container and either temporarily bypass the the MOSFETS, then charge normally, or another is to directly charge the cell for a few seconds from an external PSU, set to say 4.2V, current limited to 500mA. Note my warning regarding an overdischarged Li-Ion cell. Slight overdischarge is OK in many cases, but not severe over discharge.
I am surprised at your situation though. The battery should not suffer undervolt protection unless it was faulty or discharged to the normal low battery charge threshold of an E4, and then suffered natural discharge that took it below the safety threshold. That usually takes several months of non use. If a new battery was faulty, why mess around with it ? Just return it for warranty replacement. You do not need to return the camera. Why did you cut the battery pack open and waste $50