Arrrgh... Got the same problem and made a very bad mistake : buying another mouse after breaking the transceiver of my kit (mouse+keyboard+numeric pad).
When Microsoft says that each transceiver is unique, they mean unique.
I assumed that buying another mouse, hence another Microsoft transceiver, the previous mouse would function (as well as the keyboard and pad).
Nope. This represents quite a bit of money.
I presume that to have a single encoding for each and every mouse is meant to restrict interferences by hackers (not at all sure of that).
I also presume that if you break something (on the pad, the keyboard, the mouse), you cannot buy any replacement. This should be written
in bold on the package.
I cannot understand why the European Community accepts that such a product can be sold like this, without a warning, within it's country members.