As Mike says, the service is provided after activation, so anything upto 30 - 45 minutes after you have called to activate.
The cable normally isn't disconnected, unlike BT. But you'll get an authentication error if the hub connected to the line doesn't have a valid account (this would be the case for your old hub). This is what activation does - it links the hub you have connected to your account so it can access Virgin services.
The MAC address of the router is linked to your account, so if you change the router you need to inform Virgin to get the old router removed and the new router added. When you end your contract that router is simply barred from the network as it's not associated with an account any longer.
If you have a router which is already on an active line and working, you can sometimes take that router and connect it to another line and it sometimes works, sometimes does not. I don't know the reasoning, it might have to be in the same area. I know the same road works as a neighbour has tried it - probably because it was on the same cabinet.