that is because the menu styles are all based on #access
.
assumption: you are using the new default theme TwentyTen (?)
you could copy all the menu styles starting with #access
(from line 370 in style.css) and paste them back, and change #access
for the new div id.
if you just need to move the menu to above the header image, there are other pure css methods – unless of course you have your own reasons to make a new div.
edit:
i was not fully understanding this sentence;
I did try moving the access div in header into the new div, but the drop-down menu stopped working…?
i am not too sure about my answer;
maybe posting the code of your header (from below the body tag; including the area of the menues) might help to illustrate the issue (if the code is longer than 10 to 15 lines, please paste it into a https://wordpress.pastebin.com/ and post the link to it here)