While I advocate killing them, I strongly suggest doing it quickly, to make the suffering minimal.
But like I said - you still need to find the entry point. There is no such thing as "one rat", just like there is not one c--kroach. Because they get killed a lot they breed quickly. Chances are there's a hole somewhere behind the furniture/stove/fridge or somewhere close to pipes. Rats are also good climbers so don't just look down all the time, in basements they like to climb on pipe close to the ceiling. They don't see very well, that's why they always stay in corners, where their whiskers can guide them.