It seems that the problem was that I have messed with cart66 pages I shouldn't have.
from the installation page:
When Cart66 Lite is installed it will create a page called "store" and a few sub-pages under the "store" page. If you no longer want those pages, you can delete them through the WordPress pages panel.
It is important not to move or rename the store pages, otherwise Cart66 will not function properly. For example, if you move or rename the slug for the store/cart page, Cart66 will not know where to send folks after they add a product to their shopping cart.
To be honest, I am not sure I understand what it says here (in my mind move and delete are the same things. So how am I supposed to 'delete' them but not 'move' those pages?).
I installed everything from scratch and at the moment it works ok.