> I have not managed to get the rat to stop running in the circuit. I have done everything - I have logged every move I've made, drawn maps. I am incredibly frustrated...

First, knock down as much stuff as you can. Then, you have to get the rat out of the circuit. There is a certain direction you need to chase it from a certain location within the circuit that will do the trick. Here is the way I did it:
First, chase the rat twice from where you are. Next, circle around the circuit and chase it once. Then, circle around again the other way and chase it twice. Then circle around. Chase it once. Circle around. Chase twice. Circle around. Chase once. Circle around. Chase twice. And so on. Eventually, you should get it out of the circuit, since you cover every possible way to chase it. It's a bit tedious, but it should work.