Can we use the stored gravitational potential energy of a building to produce power?

In classical mechanics, absolute values of potential energy are meaningless. In your case of a skyscraper just sitting there, we could say it has a large positive amount of potential energy, no potential energy, or even negative potential energy. It doesn't matter at all. What is important is a change in potential energy.

is it possible to convert the potential energy of a building into a kinetic?

Based on what is said above, you would need to decrease the potential energy of the building and find a way to harness that change in potential energy. The issue is that for gravity, the potential energy just depends on the distance from the Earth, so this would mean that you would have to move the building (or at least parts of the building) closer to the Earth. The utility of buildings is typically that they remain stationary so people can use them consistently and for a long time, so I don't see this being feasible.

To see how gravitational potential energy can be converted to other types of energy in other systems, see some of the other posted answers.

An example of harnessing gravitational potential energy is a hydroelectric power plant which converts the potential energy of water falls, dams and the like into electrical energy.

As far as harnessing the potential energy of a building sitting on the ground, I suppose if you caused the building to topple you could harness the energy of the falling portions of the building. Obviously ridiculous.

All practical examples of harnessing potential energy involve its conversion to kinetic energy.Hope this helps.

Yes, you can convert the potential energy of the skyscraper into useful work. But, to extract useful work from the potential energy, must reduce the potential energy, that is: you must reduce the height of the skyscraper. You must tear the skyscraper down to get its energy.

You should note that skyscrapers aren't free and that someone used a crane powered by electricity or diesel to lift the parts of the skyscraper to their current positions. You are guaranteed to get less energy out of this process than was put in to build the skyscraper. You will waste a lot of energy in the process of converting energy from diesel or the electric grid into the potential energy of the skyscraper and then back into electricity. This would be a terribly inefficient way to store energy.

However, as noted by another answer, this is essentially what we do with hydroelectric dams. We move water from a high altitude to a lower altitude and extract useful work that is converted into electrical energy. This energy is free in the sense that the sun evaporated water somewhere and it rained down on the high altitude reservoir. So hydroelectric power is, at its core, solar power, because the sun effectively pumps the water uphill and we extract energy as it moves downhill.

Using actual electrically powered pumps, you can pump water uphill to store energy. You can use the energy later by allowing it to flow downhill.