I bought Shopping Cart when it first came out, and downloaded (but did not install) 3.5 about a month ago. When I try to open my program, it tells me the license is invalid or expired. Do I have to buy this every year?

Not likely...
I think you might have a "trial" version installed (?)
Try uninstalling and re-download (using "get support"/"orders & downloads") then re-install. This should clear that problem up for you (as well as give you the most current edition, which has had many great updates and fixes).

It should be a full version, because I paid before downloading if I remember right. But I'll try installing the 3.5 that I downloaded recently. Hopefully, that won't hurt my existing cart items/info that is entered...

Toni, were you able to install the software?