I'm glad you found your solution :)
For your information, the reason why you couldn't get the control's ID for validation using JavaScript is because Literal Controls just print pure text. This text does not have an ID associated with it...
If you had used a Label, your text would have been rendered in <span> tags, which has an ID that will let you access it with JavaScript.
In your case, you want to validate a RadioButtonList, which has an ID...
Your solution works fine for your purposes though: loop through all of the elements in the page and find a Radio Button List....then validate.
For more information check out
how to use JavaScript in ASP.NET