I don't recall any bug in 1.3.5 that prevented the radio buttons from working properly. That functionality has been around since v1.0.
Since the logic for the radio buttons is handled in the checkout template files, it would seem that you've got customizations there that are breaking things.
You didn't supply a URL, so it's not possible to help you with specifics.
Three suggestions:
a) Assuming you've used the override functionality and ALL your changes have been saved to your custom template folder and NOT merely direct edits of original files such as the template_default or classic folders, then it would be logical that you could switch your template back to "classic" via the admin, and see whether the problem persists when using the default/classic template.
But, if you've made direct edits to any of the template_default or classic folders, or to module or language files/folders without storing your edits in a custom override folder, then this easy-test feature won't be helpful to you.
b) Install a new site in a new folder+database, using the newest version. Test out the functionality you say is broken. See if it works. If it does, then you have a clear available option.
c) Compare all your files against originals, including all your overrides. Identify all differences, and fix anything that's not right. Related article: http://www.zen-cart.com/wiki/index.php/Troubleshoot_-_Diagnosing_Obscure_Issues
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