This is very strange. What is *really* strange is that PI was running on your machine.
Could you please try with another computer?
Just to discard odd things, can you verify that the MD5 checksum of the installation file is:
4db2abbde4796898e3a7b27e2ec23eb1 *PI32-win-01.00.51.357-nsi-20071213.exe
Anyway, the probability of a corrupted installation file is remote, since it includes a self-verifying routine.
I can't figure out a reason for this problem. Please tell me if you can activate your license on another machine. If you can, then copy the .pixinsight-license file to your personal directory on the problematic computer, and try to run PI. If there is a valid license file, PI won't show you the registration box.