I suspect the one showing the black is exercising a bug in that version of PowerPoint/Office/Windows. You get this sort of behaviour sometimes when the PNG handling is buggy. In essence, the transparent portion of the PNG is an alpha channel, and the alpha channel processing is buggy. It could also be a video card driver issue. I presume you’re loading the exact same file into both PowerPoint versions? (i.e. the problem doesn’t follow the file, it sticks to the one PC.) Try checking for any updates (to your video drivers, to the OS and to Office.)
Another possibility is that the PNG itself is somehow not quite correct. (Depending on what application made it, it may have incorrectly created a PNG that works 99% but not perfectly.) Try loading the PNG into a paint program and resaving it and see if that helps. I like Paint.NET for tasks like these. GIF files also support transparency, so you could try converting it to a GIF as well, and see if that prevents exercising the bug.
No answer to what causes this, but might have a simple fix. Had a similar problem recently, but with a printer output. Everything displayed on screen looked normal on a .png file, but printout was a totally black page (what a waste of ink). Exported .png file as a .jpg file. Printed fine. Try this, then import .jpg on both machines.
This happens to me when I drag and drop images with transparencies (e.g. logos) from a browser directly into PowerPoint. What helps is to save them to the harddrive and drag and drop them from their folder. The image importing via drag and drop appears to discern by the source from which the drag and drop starts.