Hi Julie, sorry to hear about the problems adding items to the Cart on your website!
Nonce errors can sometimes happen due to the Object Cache settings, and if your website currently has that enabled then that might explain where this issue is coming from.
First, navigate in your WordPress dashboard to Performance > General Settings and look for the Object Cache section there to see if it is turned on. Then, if Object Cache is enabled, go to Performance > Object Cache and make sure that Enable caching for wp-admin requests is deactivated.
I also located a guide from the WooCommerce team that provides some configuration suggestions on how to get WooCommerce to work with W3 Total Cache that offers some additional solutions you can try to get things working as expected.
Please let us know if there is anything else that we can do to help!