Pick up the phone or compose an email to your vendor. This is a warranty issue, and you need to get them to fix it.
Sure, but please note:
This is not (usually) the recommended method for using batteries or inverters, and is only intended to prove to the knowledgable user that the problem is in the precharge circuit of your PPWM battery. This should not supercede any instructions or debugging you do for EG4 and/or your vendor, and you perform this at your own risk, with full understanding of the battery, inverter, and basic electronics. [I'm not sure this applies, but here we go at your own risk.]
DO NOT turn on the inverter AC breakers, you don't want to charge or discharge the batteries.
Turn off the inverter DC breaker
Turn off both batteries breakers
Turn off both batteries BMS
Connect both batteries to the inverter in parallel.
Turn on the inverter DC breaker
Turn on the "FUNCTIONAL" battery breaker
Turn on the "FUNCTIONAL" battery BMS.
The inverter should power up properly, as you've already done this.
Now:
Turn on the BMS on the "DEAD" battery. This should not trip the BMS out. You've done this before. The battery breaker is off.
NEARLY SIMULTANEOUSLY (first) turn the FUNCTIONAL battery DC breaker OFF
and (second) the "DEAD" battery DC breaker ON.
If the system continues to work, you've used your FUNCTIONAL battery to precharge the inverter capacitors, and your "DEAD" battery to operate the system. This proves that the precharge circuitry in the "DEAD" battery isn't working.
Let us know.