I have exactly the same error code (0x80070002). I am backing up to an external hard drive. The settings have been changed and simplified, e.g. to just include music and photographs, but the error continues. CCleaner has been run on the registry.
I have tried various trial download software, with no problem. Any further advice? This does seem to be a common problem and Microsoft's support web site offers a number of remedies, including a hot fix with caveats attached!