By "it doesn't show the quick reply box" do you mean it doesn't show it in the area I pointed you to or that it doesn't show it to "guests" but normal users are allowed to quick-reply? Sorry, I'm not a mega-experienced user either, just trying to help.
Quick Reply is activated here:
ACP > vBulletin Options > Message Posting and Editing Options > Quick Reply
I realize you may know that, but just in case.
It seems to me that this option should apply to any user authorized to post to the forum, including an unregistered one who is permitted to post.
Hang in there, either we'll get it figured out or one of the big guys will happen along and give the correct answer in a line or so (oh, for their knowledge!)