The normal way to solve this problem is to use validation (or errors as you put it).
I would not advise mixing control types within a single field as it's overly complex and confusing to a user who knows what a checkbox and radiobutton are.
From a Usability perspective you should aim to tell the user what the state of the system is. So if zero selected ...
If you can dynamically add question fields, then another solution is to break it into stages:
1) Ask the null state question first with radio buttons.
2) If the option(s) which requires multiple selections is selected, direct the user to the next question.
Do you have any pre-existing conditions?
Only appears if "Yes" ...
If you are not constrained to using Checkboxes and Radio Buttons, a ListBox (aka multiple select list) is often used when at least one selection is required. A helpful reminder/prompt to the user they can choose more than one can be included.
In HTML, it's represented as (from W3Schools)
<select name="cars" size="4" multiple>
I designed a couple of multiselect dropdowns for a client who has a lot of them with a huge amount of possibilities to select from. There are multiple ways of making clear the user can choose various options. What I usually do is when the user hits the input field, the dropdown pops up and stays open for the user to choose from the list. When the user is ...
Multiple selection needs to be coded in so that it's possible. How developers [unless that's you] do that may influence your design/placement approach.
EG, in the page here, it is fairly intuitive once any item is selected, it appears along the top. Or if coded to feature check boxes in the drop down, that's also intuitive once ONE checkbox is added to the ...