Chimney flue not drafting

Boiler and water heater in basement of philly row home. Chimney is pictured. There was a cap but i removed it to look for obstruction. It's wide open. The boiler is 140k and the water heater 36k. I've lived in this house for 4 years and never noticed it before. Doesn't mean it wasn't happrning. Monoxide detecrs are new and not going off. When the boiler fires the room gets very humid. The damper valve is opening and closing properly. If you put a match by the water heater it blows it out and the smoke comes into the room.

Pilot stays lit.

Two sides of chimney are on cold walls

Here's a video https://youtu.be/l42eXDYj_SM

http://imgur.com/a/gK5Ze

Still back drafting. Boiler flue pipe have condensation on them.

I closed off half the chimney Cap to help slow down the cold air but it has not effect.