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SIGH ..... back to where I started :(
Tried that alternative Backup programme, but after 30 mins or so, it was still initialising - so ended up uninstalling it.
I installed Avast and various other bits and bobs, but something didn't agree with IE, as it wouldn't work properly, so ended up uninstalling Avast (yea I know IE is tosh, but I play an online game where I need to log on 2 accounts simultaneously and I found IE works best).
As for the connections, etc .... they aren't an issue, as I run the programme without the drive attached. The programme opens fine on my partners' laptop but not on mine. Obviously something is conflicting with the programme - it's just a case of finding out what.
I have other WD programmes installed on my laptop (WD securities and WD Drive Utilities). I think I might try uninstalling all WD-related programmes, then just reinstall WD Backup and see if that works; although everything worked fine before, so I can't see why they should be conflicting with each other now??
Failing that, I'm going to pass my laptop to my brother in law - he's a bit of a whizz with laptops and PC's :)