I can run neither Paint Shop Pro 3 nor Paint Shop Pro 4 in the Windows 8 beta. They both fail with the same symptoms: the cursor spins for a few seconds, then nothing--no error dialogs, no popups, nothing.
I've contacted support hoping for help but--hey, this is a surprise!--they said "At this time we cannot offer any advice on how to run Paint Shop on Windows 8 preview edition." So, thanks but no thanks.
I'm enjoying my PSPx4 CD; it's serving very well as a coaster. Since they never fixed that stupid PSPx3 copy and paste bug, I'm kind of running out of enthusiasm for chasing this particular screw-up.