CainIV - 5:44 am on Mar 11, 2010 (gmt 0)
If I understand you correctly, Google has spidered the internal folder and its contents, as opposed to what is at the index, which is of course a duplicate of what is in the NEW folder.
What I would do if the website is small, is
301 permanent redirect the inner pages in NEW to their exact duplicate in the root of the website, and leave the NEW folder there for now.
Add the link canonical tag to the index page in the NEW folder and point it at the root of the website where the canonically correct page is:
<link rel="canonical" href="http://www.mywebsite.com"/>
Check the stats code returned in a header check by typing in
into a search engine, and enter in the full url to the index page in the NEW folder.
The tool should show that there is a permanent 301 redirect to your domain root, and the domain root default page returns a 200 OK status.
Also check that there isn't anything in robots.txt blocking the index page in the root of the website.
The combination of these items should place the correct value to the root of the website. Once the main pages are back, I would then build some links to the main pages and remove the NEW folder and redirects.