Can't install Print Shop Deluxe 20 on my computer.

Afraid so.
If it's possible, reinstall XP.
If your system came with Vista, I'd go buy XP.
Purchasing software of any kind, always look on the package to see what it's compatible with.
Not a lot are compatible with Vista. If you feel Vista is amazing try another alternative. Download and install Windows 7. The Beta is free until June 1, 2010. Giving you plenty of time to save up for an OS.
Just be warned, what didn't work on Vista may not work on 7.