Why couldn't my battery pack start my car?
Kirchoff’s Law would explain the failure if you had any measurments.   Even a lead acid battery might not have enough with poor contacts or cables and good contacts might fail with a high ESR battery.

the best approach is to transfer the charge from the external to internal battery for a few minutes to eliminate the external ESR issues.  The internal battery will have high ESR with low charge and the action is visa versa with external charging.

with sufficient charge Q=CV and low ESR the voltage sag = I* ESR should be less than 40% and it should start.