I understand that your cart and search icons are not being displayed on your site, is this correct?
After inspecting your site by the browser console, I am able to see that there are some Mixed Content warnings which essentially means that some of your content is being loaded via HTTP while your site is in HTTPS, as can be seen in the screenshot below:
Thanks for providing an update, and sorry to hear that the plugin has not helped toward resolving the issue!
After checking your site through whynopadlock.com, I am able to see the files containing the Mixed content warning messages, as seen in the screenshot below:
As a next step, I’d suggest reaching out to your host, which appears to be SiteGround, and asking them to check your sites HTTPS. They may also be able to assist you in updating the URLs of the insecure files to use a secure URL.