I have fixed this problem in the past by resynchronizing the keyboard & mouse to the receiver. I'm presuming that your keyboard & mouse are within 5m range of the receiver? You may need to click start & then onto Devices & Printers to select your keyboard & mouse (by right clicking & then selecting 'remove device'.
You said that your batteries are fully charged but I have noticed that lower mAh batteries are a bad choice for modern devices. Your batteries might be 800mAh but you will definitely benefit from using 2000 or 2450 mAh rechargeable batteries. Your batteries may also be old? Out of interest, have you tried the batteries from the working mouse?
Is the RF receiver close to another electrical device? Maybe a power source or radio/tv aerial? As this can cause interference to your RF receiver.
Is there another local keyboard & mouse that is being used by someone else, which could be interfering with your setup?
Wireless landline phone can also cause issues if the receiver base is too close etc. A few things there for you to check & try.
I've removed the device several times and reinstalled the drivers.
The batteries are standard Duracell batteries which i've had no problems with in the past. Likewise the receiver is near (within 7m) of a TV and plug sockets....but again this isn't something new and the keyboard has worked fine over the last 3-4 years.
I think maybe it has just broken and needs replacing. I just hope it doesn't happen with any new device i buy.
Yes I think it could well have come to the end of it's life & maybe time to purchase a new one. You might want to consider a bluetooth keyboard & mouse this time around? They function a whole lot better than the RF types & have a much better lifespan, speaking from personal experience.