Did they come separately or were they in the same package? If they weren't in the same package, you can only use one dongle and the differing hardware will be tuned to the different dongles. Make sure to have the most current drivers and Microsoft Keyboard and Mouse Center from the Microsoft hardware website. There are fake drivers out there that really aren't the latest but which have had their version numbers bumped up to get people looking for newer drivers to install something malicious. The driver should contain the words "USB Dual Receiver" in the driver name in Device manager.
Did you install the drivers while you had the dongle plugged in? If so, you need to completely remove all the drivers and Microsoft Mouse and Keyboard Center. Use the original keyboard to install the drivers first, and then, after the computer is restarted, remove the original keyboard and insert the dongle, and wait for the system to recognize the hardware and install the correct driver. Try also removing all keyboard drivers and rebooting. Sometimes conflicts arise. Make sure that no remnants of the Microsoft drivers remain on the hard drive. Use Device manager to delete drivers completely from hard drive before trying this. If any traces are left this will not work.