None of that "Canada 310 N14644" is relevant to the model number. That's all regulatory agency numbering.
Connecting your device to Home, if the system really is empty, should cause Home to offer you at least the operating software. Your bigger problem will be your map / map folder, which is keyed to your specific device. If you never took the time to make a backup of your device as a whole, or at least the map folder, you're in some real trouble ... you'd need to buy a new map for your unit, unlesssss... you have a backup you don't know about.
Did you take advantage of the latest map guarantee (for the freshest current map) when you first bought the unit? Or did you ever buy a map update for your unit? If yes to either of those questions, do you still have access to the PC that was used with either of those were done? If so, there's a good chance your map can be recovered from your PC once you have the application restored to your unit, and we'll explain how once you've replied.