Condensation running down pipe connecting furnace thru ceiling to chimney

I had a new downflow 80% efficient furnace installed in 2006. I don't use it regularly as I normally heat my home with my woodstove (separate chimney). But I have used this new furnace many times during "in between" weather, and when I have been out of town. It has always worked fine. Then in 2011, I used the furnace regularly for a few months that winter. I noticed that I had water or condensation running down the pipe that goes from my ceiling to the furnace – it would happen after the furnace ran for a bit. It got to the point that I had to put a pan on top of the furnace to catch the dripping "water". My immediate thought was that my chimney stack must be cracked as I know the hot air from the furnace meeting the cold air in the stack (if it were cracked) would cause condensation. But after taking off the chimney cap and checking – the stack is fine. My chimney cap was blown off during a windstorm, and now is slightly damaged and sits a bit lower than previously. Could this be causing this problem? I was told by one furnace guy that my chimney stack is too large, and that it needs to be lined to make the opening smaller, and to replace the chimney cap. He swears this will take care of the problem. I'm just wondering why it took 5 years before I had a problem. Could it be because I was not running it 24/7 like I started to in 2011? I hate to pay for all this work if that isn't the solution?