I've managed to get the desktop back to its (non-functioning) working point by doing another system restore to undo all the various things I've tried.
However, it still won't connect.
Significantly, when it starts up the "troubleshoot my connection" link appears instantly - before I've even had time to connect the BB.
It's as if the software can't speak to Windows, if that makes sense.
PS My old pocket PC connected fine to the USB point, so it's not a hardware fault.