Now, a few days later, I have charged module 4 several times for some hours reaching a reported SOC of 44%. However, always when I continue on the next day the diag software reports cell high about 3.4V and low about 2.0V and the module voltage is several Volts below I left it with the previous charging. The BMS sometimes has become inactive again, probably due to module voltages below 12 V. Green LED is then either solid on or long time on with short off times. My understanding is that it should blink about once per second if the status is ok.
So, I have come to the conclusion not to continue like this. The cells are very likely damaged if they rested totally discharged for 2 or 3 years. And I don't want to risk that they blow out or even catch fire.
I might disassemble one or all modules in the future to diagnose it or replace cells when I find the time to do it.