We've had the same issue - after adding a product to cart in Presta 1.7.6.4, the cart was empty. It happened only while being a guest. I started debugging in controllers/front/CartController.php and found out, that for some reason every time I added this product to cart, new cart has been created and id_cart stored to cookie. But immediatelly forgotten and after adding the product another time, new cart was created again and id_cart stored to cookie again and so on.
Then I've found it happens only with specific product and after adding a different product into cart, I can also add the problematic product without any issue. So I examined the difference between cookie after adding the problematic product and non-problematic product. I've discovered, that after adding non-problematic product, the cookie contains also id_guest and id_connection while when adding a problematic product, it doesn't containt these two.
Finally, I've found the reason - and it's been funny trivial - the problematic product had too long description (summary) - 995 characters as counted by backoffice, but in fact 1221 characters when viewed as HTML source including HTML tags. After shortening to less than 1000 characters including HTML tags, everything started working fine. So due to that long summary, something broke during the proccess of adding to cart and id_guest and id_connection was not saved into cookie and and the created id_cart was not paired to the guest session.