Hi Bob,
Thanks for your answer. Unfortunately my problem is a bit deeper than this:
1. Yes, I have a base tag.
2. As I say, I have moved OFF apache and ON to nginx, so htaccess is not relevant.
Here is the site (You MUST access it without www - if the access it with WWW, you will see the "original site", on apache, all working.):
http://financetrails.com/
You'll see, by viewing source or hovering over any links, that each and every href="" is empty. So, it is an issue in MODX itself, not with rewrite config at the server level. If I turn off FURLS, the hrefs are populated correctly, for example, index.php?p=6