Graham:
Which version(s) of NeatReceipts did you install?
And have you turned off the UAC while you are performing the install and uninstall operations?
We can start there, and move up to the manual uninstall methods including removal of MSDE or SQL Express and Windows Installer Cleanup after NR directory removal.
Or if you need immediate response, you can give tech support a call and they can walk you through everything.
-Jonathan Hardison-