SIM card holder was prime suspect. Sorry, I forgot to mention that I re-soldered the holder. Cleaning included.
Ok, googled SIM pinouts, SIM holder pinouts. I was not able to find any SIM holder pinout similar to this case.
I tried to poke it with scope anyway. My findings: there is activity starting couple soconds after turning DUT on, high appears to be 1.8V:
pin 1 = ground
pin 2 = Vcc? gets up first, stays high
pin 3 = ground
pin 4 = I don't know, gets up last, stays high
pin 5 = seem NC
pin 6 = should be clock ~3MHz; it does the clock thing for ~3-4 seconds then goes low
pin 7 = should be data line; does something while clock is on, then stays high
To understand the sequence of the events I did it in pairs also: pin 2 gets up first, then 7, then 6, then 4.
I did SIM holder pic and scope screenshots, see gallery.
I should capture the whole thing probably to understand the ending. But for that I need to do some reading first, I'm not that proficient with scope yet

Any feedback appreciated!