You should have left the trial version active and just used the activation code to unlock it (or whatever Corel calls it).
How did you uninstall the trial version? Have you checked the install/remove programs to see if it's still there? If so try to uninstall again.
What security programs do you have running? Firewall program? Antimalware?
Have you turned off UAC (User Account Control)?
Have you tried running the installer file as an Administrator? (right click, run as admin or properties> run as admin)
You may try creating a different account in Windows and installing in the new account. If that works you'll then be able to delete the new account after you verify you can use the software in the main account.
"Smoke me a kipper, I'll be back for breakfast."