Having built a 70' narrow boat in a previous life (oh god, now Jimmy the builder will think I've got a beard, smoke a pipe and wear slippers).....
Assume you haven't been on the boat for ages. If the pump has been running long enough to flatten the battery make sure you haven't got a bilge full of water somewhere. It could be the pump got air locked and just ran on. If it hasn't been used for ages more likely to be seized and that wouldn't flatten the battery.
Pump likely to be by your water tank or possibly close to the first outlet (sink). If you do need to replace the pump use it as a chance to make sure your installation is correct and adjusted properly. On the high pressure side of the pump there should be an accumulator tank (big sphere with a bladder in it). Water pumps into the bladder, void outside the bladder is under pressure and the trick is setting that pressure just right a bit below that of the pump. There is a shrieder (sp) valve on the top so you can adjust it. The idea is the water pump fills the bladder. When you turn a tap on the bladder shrinks back to provide the water and the pump doesn't run. Eventually the bladder empties sufficiently for the pump's pressure switch to trigger and it runs until the accumulator tank is full again ( hence why the pump continues to run after you've turned the tap off).
The accumulator tank also smoothes out any pulsing from the water pump. Your pump will last longer and you can turn the tap on in the middle of the night without waking people up.
Sorry if I've just taught my granny to suck eggs but you see lots of boats either without accumulator tanks or with them set incorrectly. If you replace the pump a lot of people don't realise or forget to re-adjust the pressure in the tank.
If it was an air lock then the pump would run on continuously. Obviously check any fuses or circuit breakers (trip and re-set them, don't just rely on the fact they look fine), but by the sound of things the pump has siezed. Hard to life but 6-10 years wouldn't be out of the way. Not sure how old your boat is.