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The Export PNG dialog is probably opening in the docking area, on the right side of the window. Look for it over there. If you don't want it to be docked, you can undock it. Grab the title bar (which has a tiny triangle and tiny x box on the right side of the bar) and just drag it away.
If you don't see it there, it's possible it's miminized. Look on the right side of the docking area, and there should be a little icon and the text "Export PNG Image". Click on that and the dialog will open. If the dialog was docked when it was minimized, it will open in the docking area. If it was floating, it will float as before.
If you still can't find it, there's a chance it's not opening in the viewable area of the screen. That can often happen if you are using Inkscape with a multiple monitor setup. Or if you used to use multiple monitors.
Let us know if you find it in the docking area. If not, we can still help you find it.
Edit
Wait, which button does nothing? Do you mean that you have the dialog open, but when you click Export button, nothing happens?
If that's the problem, then you need to look in the location which was showing in the Filename field, when you clicked export. If you don't change it, then by default, I think it is saved in your C:/Username directory. Otherwise, you can change the location to have the PNG saved wherever you want. To do that, click the Export As button.
Edit #2
Or could you be talking about Edit menu > Make a Bitmap Copy?
