I don't want it to seem like we're ignoring you but this one is probably better addressed with a phone call to Adobe Customer Support.
Installation issues get free support and they can talk you through things to look at in real time rather than the days it would take to cover bases (probably unsuccessfully) on a text based forum.
FYI, this sounds unusual. What should happen is that an installer should pop up as soon as you click on the completed download. If that's not happening then this is a weird one.
Which version did you buy? And where were you downloading it from?