Hi Stephane,
All the below assumes you feel there is some value in keeping the original website live at all.
My first reaction would be to do a full review of all your old content and carefully consider which ones may have been hit by Panda - is there keyword stuffing, content duplicated from other sites, thin content...etc? Then either fix or completely rewrite those.
After that you should avoid publishing duplicated content so my view would be
1. Remove the rewritten/fixed articles completely from the old site
2. Don't implement the 301 so you don't get any redirected bad Penguin vibe
3. Put a block on those URLs using robots.txt
4. Remove the URLs from Google's index in Webmaster Tools
Then you are free to publish your new, Panda-friendly content to your new website.
Not sure what other mozzers would say, but that's my view. This is not about 'spinning content' but removing poor content and republishing great content. Hope it makes sense.