It definitely should not.
Something else is going on on your system that we probably can't diagnose on this forum. Have you contacted Adobe Tech Support?
One possibility: What resolution is your monitor set to? If it does not meet Premiere Elements minimum specs, the program will not be able run.
Steve, I followed your suggestion and contacted Adobe's "chat" help. It took several hours ("chat" is slow), but the support guy did an excellent job of finding the needle in the haystak.
This problem does not effect any other programs on my computer except PE-11. Yet, there is an unholy interaction between PE-11 and two of the Windows desktop themes: "Windows Classic" and "Windows 7 Basic". If either of these two are selected, PE-11 becomes unuseable, at least on my computer -- and my computer's specifications far exceed the minimum specifications for PE-11. In short, the workaround is to avoid those two themes.
The cause of the problem is obscure and difficult to locate, so I hope this post saves a user some grief in the future. Hats off to Adobe support for finding a workaround for this bug.
Thanks for reporting back, Reed! Hopefully, that will help someone else avoid a lot of frustration.