I have the DiNovo Cordless Desktop too, the old version (LZ845AG).
The problem reside in the dual mode functionality of the USB dongle. It is a full btusb dongle, but it has a second operating mode: it works as a (non-bluetooth) HID device.
This is neccessary if, for example, you want to enter BIOS with the keyboard. There is no bluetooth stack available at BIOS stage, so the dongle works in HID mode. Otherwise you could not use the keyboard in BIOS / DOS / any non-bluetooth environment, so the dual mode does make sense.
However, full functionality is somewhat broken (again) in 12.10., depending on your setup. I have tested 3 choices so far:
1.) You are working on a non-dualboot machine: No problem. Just bind the keyboard / mediapad / mouse once. Re-insert the stick if it does not work. Re-insert the stick while pressing the red button on the stick if it still does not work (this will force bluetooth mode manually). When the bluetooth icon finally appears on screen (top bar, left to the time clock): Press the red buttons one the devices, then use the bluetooth icon to add the devices, one by one.
2.) You are using a different usb dongle with the hardware: Works too, see above, but you need additional software on dual boot machines, e.g. for Windows. May be tricky there, but works for Ubuntu just fine.
3.) You have a dual boot machine and want to use the original usb dongle as well as the standard Logitech Windows software: At least with my DiNovo (old version) the problem is now that you are forced to re-bind all of the devices everytime you switch operating systems. There are rumours the newer DiNovo does not have this problem, but I did not find a way around it with my old DiNovo so far. Very sad, as the DiNovo is not the cheapest keyboard / mouse combo around at USD $180.
So everytime you switch, enjoy the hen and egg problem: Try to add keybard and mouse in Ubuntu without having keyboard nor mouse. Good luck. ;)
On older Ubuntu versions you could circumvent this by uninstalling the Logitech software in Windows and let the DiNovo run in HID mode under windows, and in Bluetooth mode in Ubuntu. For some reason, this does not work in 12.10. anymore.