This is a pretty fun story. Using Inkscape, clicking the Export PNG Image... option in the File menu appears to accomplish nothing at all. However, I realized the reason is that the dialog is docked in the right side of the UI.
Amazing how something as small as this can break your intuitive work-flow as you use apps that are unfamiliar. Usually I say to people:
once you have seen one app, you have seen them all.
This is a oversimplification of the skill involved, of course. Nevertheless, it is actually not far from the truth. Once you have learned to use Illustrator, you should also be able to use Inkscape. In my opinion, the free programs certainly have their place, especially when you both work with Linux and Windows.
I work with both Windows and Linux, and often I create .svg's from windows using Illustrator, which I then need to use in Linux (kubuntu in my case). Since Illustrator is not directly available in Linux, I use Inkscape to open my .ai files.
Not the only one
I am not really complaining though. I think this is one of those things, that you just have to get used to.
The problem with a lot of Open Source software, is that the GUIs tend to do things in non-intuitive ways. For a long time the GUI-designs has really been shitty compared with Windows, however, I do think that things has been improving. Plus. In a lot of cases, you just need to get used to how open source software does things.