Condensation running down pipe connecting furnace thru ceiling to chimney
Sounds legit.  As you decrease the temperature of air inside the chimney you decrease the flow rate out of it causing the mixing with cooler air to happen in the chimeny rather than out of it.  It could be that this didn't happen in 2011 because of warmer outside air temperature, different humidity conditions, or that your exhaust was running hotter/faster then.  If you use the formula on wikipedia you can calculate your desired chimney cross section (just remember to use metric to stay consistent).  Also the damaged cap definitely could slow your flowrate which could contribute to this issue.