Hi,
I noticed that it’s not a problem related to WPC, but it should be related to other plugins, to test it, I have created a new product:
http://evacuatieman.be/product/no-wpc/
Where WPC is not used. You could also try to disable WPC and you get the same results. Products are not added to cart.
I think the best thing you can do is:
1. Get a previous version of the website
2. Install it in another place
3. Update the plugins one by one to find which one has the problem
It could be a theme update error also.
Remember that is always a good practice to do a backup of the website before any update.
if you need more help, please ask me
Best regards,
Enrico