Click on the Start button, then on Computer.
Double-click on the icon for your hard drive.
Double-click on Program Files.
Look for any folder labelled 'Corel', 'Paintshop' or similar.
Right-click on any relevant folder and select Delete.
Restart your computer and try installing again.
NB: The foregoing assumes that you really have uninstalled the program in the first place - look in your list of installed programs to check - AND that you've not got any other Corel software on your computer.
Alternatively, or as well, install CCleaner to see if it will clean up the entries which are showing Paintshop Pro to still be present:
http://www.piriform.com/ccleaner
If all else fails, try a different photo editor. GIMP is similar to the might Photoshop but completely free:
http://www.gimp.org/
(However, just like Photoshop, there's a steep learning curve to get the very best from it).
Serif Photoplus SE is another great freebie, which is easier to get to grips with but still meets the needs of most home users well:
http://www.serif.com/free-photo-editing-software/?MC=FSSPHOTOPLUS
Chris