Well, you can easily workout on this issue.
What you must have done is used 'Visible=false' as one of the attribute on dropdown. This would not just hide but also let the control not participate in page rendering. It will be completely missing and thus no accessibility even via JavaScript.
Instead, use style display property and all will be good.
myDropdown.Style.Add("display","none")
myDropdown.Style.Add("display","block")
In JS, just pass on the ID and you will get access to the control to play.
Try!