My words literally betray me.
From my first read of the rulebook, it says that when the Runner accesses cards in HQ or R&D, if it is an agenda they can steal it or pay the card's trash cost to send it to archives. Since ICE doesn't have a trash cost (that I have noticed) does that mean that nothing happens if the Runner access a piece of ICE in HQ or R&D?
Correct. Assuming it is not a demolition run.