Thanks esmi & shane for your replies.
I took the server offline for a while and removed the HDD to do a complete virus scan - just in case that might have caused the problem but it came up completely clean.
So far I have this:
Totally new install of WP 2.9.1
Completely empty database.
Using default theme.
No added themes
No added plugins
No active plugins
I modify wp-config-sample.php with details for my database and add the unique keys.
I go to mydomain.com/wp-admin/install.php
I enter the blog title and my email address, then using the generated password I login... all good so far.
I then go to Appearance > Widgets... and find I can drag n' drop anything.
This is the same for IE8 and FF 3.6
Javascript is enabled in both browsers.
Everything I'm using...
Windows 2008 Web Server
IIS7
PHP 5.2.12
MySQL 5.1
Firefox 3.6
IE8
I have other WP installs on this same server and I have the same problem with all of them - i'm certain the widgets for these sites used to work (drag n' drop) but now they don't.
@esmi if you need to contact me through regular email, I can set up another test install on a different domain name and send you the login details...