Yes, the golden key is already spent, the inner part of the chest repaired - I just need to close it.
(If it helps, the only mentionable inventory has Marco: smartphone, letter, screwdriver, map, badge, wand)
to close it you need a SECOND golden key that you can have from the Rector - asking him what he still need to know to be helped
if he doesn't still help you you may have not yet discovered that there's a golden statuette on the ISS - that you learn from Samuele (thru Andrea) if Andrea asks him about Tarrisi - knowing that Marco can correct the Rector when he says everything is still find and then he will help
I'll check it (to see if there's not an error somewhere) but this should be the correct sequence
I hope this is the missing detail