I sure hope that's not dangerous. This might be a time to call in the pros. Blocking the vent could cause some serious trouble, as could leaving it open if it is allowing dangerous gasses into the basement area.

Is your house old? That second flue could be for a boiler or furnace which was removed.

Could it have been for an older gas water heater or furnace?

House was built in '92. Must have been a furnace before they went with central air and heat. Cold air comes through into the basement, it should be capped on top.

We have a wood burning fireplace insert, with one flue going up from that. I've been wondering if that second flue somehow introduces cold air, but if it's going its separate way from the basement to the roof, probably not.

My problem might be cold hearth syndrome. I have no idea what's surrounding the flues, but if they're not within the home envelope, as they call it, I'm doomed. Cold air comes from everywhere, even through the bricks.

I just need to win some lotto money, then tear out that wall and make an addition.

How is your house heated today and how do you produce hot water? The house may have been built with a gas 80% efficiency gas furnace which used the exhaust vent you are seeing in the basement. This could have also connected to a gas hot water heater. If the previous owner converted the heating and how water to electric, then this exhaust vent is no longer needed.

Does you fireplace have a chimney damper and do you keep it closed? Have you looked into installing a fireplace door?