hi there,
if its in the basement, i am thinking whether the basement has been tanked properly, we had a brand new buils clean last month, where because of a water leak in the kitchen units the white melamine coated chipboard on the backs of the kitchen units had gone black, like spores, and when you first wipe them they just smear, it needs a bit more elbow grease.
combined with the greening on the radiator, i would be looking at the black soot like substance to be damp spore growths, another common place is in the bathroom, on the cold water pipes, as the heat in the bathroom, added to the cold water pipe,sometimes creates the right conditions, ie condensation for growth.
i could be wrong, but thats what weve experienced in the past
regards
martin