Pair the wireless Microsoft Keyboard+Mouse to a different mouse

Tricky, since the Logitech seems to be using a proprietary radio protocol, I think. If it was Bluetooth I would not expect this type of interference since that uses the whole of the 2.4 GHz band, changing frequency 1600 times a second so it is only ever on one particular frequency for a very tiny fraction of the time.

My guess is that the Logitech is using one or one of a very small number of narrow-band frequencies, and this happens to fall within range of your wi-fi signal. A more reliable way to beat the interference would be to change your wi-fi access point (or router with built-in AP) to a different channel, as far away from the current one as possible (eg go from 1 to 11, or vice versa).

OOPS... The mouse with low battery was in fact a mouse that came with the keyboard and had been put into a drawer nearby - in 2006!

We happened to find it and THEN my friend remembered that there was one.

SO... she was NOT picking up something from a neighbor.

I'm still wondering what binds a given mouse / keyboard to a given receiver and how does that work if more than one is in the same range.

I also wonder why with the new computer it decided to pickup that mouse after all the years.