Thanks for confirming the ECU story, it starts to make more and more sense.
I disconnected and cleaned connectors on all cables including earth. So all the cables I'm about to replace with the upgrade kit.
Yes it's a Lithium, and I've tried warming it up, didn't help. And after some starting attempts one would think the battery also warms up?
I think the starter is not to blame, because when I shorted the solenoid it went round like never before... when I'm typing this I think it's really just too much voltage drop over the solenoid? I measure 4.7 Ohm over the solenoid terminals when its closed, read that "around" 4 Ohm is normal.