EDIT: The OP indicated that by 'mass damper system' he meant a damper of the kind usually used to stop skyscrapers from swaying. This only adds to the weight of the structure. With that in mind:
As soon as whatever wizardry you're using to support the structure fails.
Seriously. At the dimensions of the structure you've got, either this is some insane super-alloy of steel that is strong when hammered out to wire thinness, or you've got antigravity technology reducing the weight. As a comparison: The Burj Khalifa, standing at a measly 829.8 m, has a dry weight of 500,000 tons. That's a masterpiece of engineering, it's a slender spire, and it's already having to deal with some of the most extreme mechanical stresses we've ever dealt with as a species.
Your pyramid is much taller, much wider and has a cladding of slate for goodness sake (see type_outcast's comment on the question for more on that. I just spotted it.). Regular steel won't hold up under that. It will crumple under its own weight or sink into the bedrock below. Even mountains can't get that tall without other mountains shoring them up, and they're solid all the way through.
Which leaves us with some form of either:
A: Magically strong steel whose mechanical properties are unknown but somewhere on the far side of ridiculous. In this scenario we can't estimate how long your structure will last, since its skeleton is basically badass.
B: A magical anti-gravity device making the whole thing stand up/not get flattened by weather systems which is presumably powered. As soon as the power goes out, this stops operating, causing the pyramid to collapse.
Edit No 2: The OP changed the height of the pyramid (which doesn't help) and suggested that the structure could be supported using a central column.
Just for fun: lets do the maths on a central column. If it's a 1m2 column that's 2001 m high, we can easily work out the force being put on the bottom meter of the steel as 2000 * 8000 * 9.8 (Height * density of steel in kg/m3 * g). This comes out to 156.8 GigaPascals. The highest compressive strength I've been able to find for steel is 152 GigaPascals, which means that even in an ideal world, with no wind, shear stress or additional weight, your supporting column crushes itself under it's own weight. Adding extra columns or support struts won't help, they just make the problem worse. And that's before we get to any of the other architectural problems the pyramid has.
The lower struts of your pyramid are the first to fail, especially on the side that faces the sea. The weight of the structure above them essentially flattens the entire bottom half of your pyramid, heating it by an appreciable amount as it does so, and turning the lower levels to molten slag. The upper levels warp and buckle, slowly sinking and cracking, with those struts nearer the bottom becoming bendy and rubber-like. A wave of semi-solid steel and shattered slate spreads out over the former state of New York, washing everything (buildings, soil and even the top layers of bedrock) before it.
Eventually you're left with the largest, most bizarre piece of modern art ever. At it's heart lies a slowly swinging pendulum that weighs exactly 1852 tons.