How do you have the Premiere Elements 9.0/9.0.1 Welcome Screen set up?
Well I've not paid attention to this before but the same box as on the screenshot is ticked.
Let us assume for now that you have it set for "Just Show Welcome Screen". If so, and, when used
that way, do you arrive at...
Yes, this second screenshot is where I arrive. And you can see the grey color around it. This grey color remains there even after clicking "Ok".
[...]and in the Adobe Premiere Elements 9 are these two .exe files. Try each by
double clicking and observing the results.
Nothing, I'm afraid.
If you see the second screenshot details (but no new project dialog, can you
click on File Menu/New/Project (or use Ctrl +N) to bring up the new project dialog?
Yes, but no improvement after that.