Normally, when a user registers through the plugin, he is given the role Support User. This role has special capabilities.
If your users get the error message “You do not have the capacity to open a new ticket”, it means that they don’t have the special capabilities.
Here you have two choices:
If you don’t know how to add new capabilities to a role, I suggest you use a plugin like User Role Manager and give the desired role the following capabilities:
Do not give your users more than those 5 capabilities, otherwise they could get administrative privileges.