Can one USB receiver connect both mouse and keybaord?

Logitech make a 'unifying' USB transceiver which works with selected LOGITECH products. Their concept is that one can easily use the same mouse and keyboard at different locations, having a transceiver at both ends.  It also works for instances like yours where one of the devices breaks and you have to replace it.

http://www.logitech.com/en-us/promotions/6072?wt.ac=ps|6248|Unifying

It doesn't solve your problem now, but you might want to consider a change of make in the future..

It is not exclusive to Microsoft, few wireless receivers can be reprogrammed without specialist equipment. They lack the circuitry to interface in that way to the USB bus which would be built into the production line.

The Mouse/Keyboard itself would require extra components and therefore cost to set it into pairing mode to allow the receiver to find it.

There one programmer can pair up tens of thousands of devices which is far cheaper than including it on every set. Even a few cents saving per pair adds up when they make so many.

No unless you buy a Wireless Desktop kit which includes both Mouse and keyboard paired to one receiver.

That's the point, there is no way to re-pair either device at the desktop which done at the factory.

Okey...thanks. But do you know why on earth MS does this...