Nothing to do with Vista, it's because PI 10 is older than Vista and built for Windows98/Me/2000/XP, Ulead did not write it to work with an OS that wasn't even finished and released.

Now Corel own PhotoImpact and is at version 13 (X3) which is built to run on Vista.

You can try this:
Remove PI entirely (uninstall)
Reboot the PC - then install again but this time as Administrator (right-click the setup file and choose Run as Administrator)
Once done, start the program for the first time in the same way from the desktop shortcut (or programs menu).