Basically, when the submit button is clicked, I want the script to verify a radio is checked, if one is checked to do nothing.
If one isn't checked I want it to post an alert message.
I would change the line if (radios[i].checked) form Valid = true; to if (radios[i].checked) so it becomes true with the value of the checked item. Also, always use braces, even if there is just one item.
Since then developments in Java Script have introduced ways to perform radio button validation in far less obtrusive ways however the less obtrusive code is slightly more complicated and has a significant overhead if you do not use that approach for all of your field validations (as you ought to).
Of course many people still use this means of validating radio buttons simply because the code is easier for them to understand.