The long and short and final answer. Each receiver (dongle) is unique and paired at the factory. If you have a spare receiver, throw it away. It is worthless.
This is false information. I have two sets of the Microsoft Natural Ergonomic Desktop 7000 Keyboard & mouse and I have successfully paired one with the receiver of the other. It's actually quite easy. You just hold down the little pairing button on the keyboard
or mouse at the same time you hold it down on the receiver.
I do believe, however, that these receivers are unique to Microsoft's wireless keyboards. I'm hoping that maybe the close cousin, the Microsoft Wireless Rechargeable Laser Mouse 7000, may happen to be cross compatible and have ordered one with the intention
of testing it. I don't have any certainty whether it will work though.
In any case, I still share the frustration of all who have posted here. There's an awful lot of people that have lost the use of their otherwise good keyboard and mouse simply because they lost the receivers. If Microsoft could have just picked a more standard
receiver or purposefully produced more receivers than keyboards & mice, they could have prevented this. If nothing else, for customer satisfaction it seems like it might be worth it to make some more, but I guess it could be expensive at this point.