If your contact module is not working, then one of the first things to check is the field ID of each field in your form that you have created.
When you open the Contact Module, and go into the settings for each field by clicking the cog icon;
At the top of the field settings, you’ll find the field “Field ID”, which should be a unique name for this field. In this field you can only use standard English characters, no special characters, and no spaces.
So for example “Post code” is not possible as field ID, but “postcode” is.
So if your contact module is not sending messages, please check your Field ID’s first :)