I've reconfigured a Wordpress site to use https and although there are no http links appearing in the html source Chrome still says "connection not fully secure".
I've read this post and I find in Developer Tools > Network there is a jpg file listed as being on an http connection. However I've changed the only reference to this file in the database in table wp_posts in field guid to be https, refreshed the browser cache but it is still listed as http although not appearing in the source.
Other non-wordpress https sites on the same server show the secure sign so the certificate must be installed correctly.
I've used the online checker at www.whynopadlock.com and the only item it flags as a fail is the jpg image, which I've changed? Is there a WP cache, I can't see an cache plugins in admin.
Try to search for all http:// version of the website in your database but also, change the name of the website in the main settings to https AND flush your permalinks if you haven't in Settings -> permalinks -> click update.
If it doesn't change anything, maybe the file is hard-coded in your template file? Another script could load the file via ajax you wouldn't see it in the source code...