It is possible that in some instances a Site User can navigate the site, add products to their cart and place an order and the storefront might not show any prices on any of the pages to the Site User.
This is likely because the specific Site User does not have the option to view pricing enabled for their account. To correct this, go to SiteName > User Management and edit the Site User. Check the box for "User Can View Pricing" and save the settings.
Once this has been enabled, the Site User should be able to see the prices on the site.