how do i get the rat out of the prison compound?!

Become a stony and talk to all the stonies. One of them (near to the Prison Compound) gives a code, which will be random each time. This refers to the sequence in which you should press the buttons outside Dilberta's prison.

However, that's not all. You also need to go to Glitter Gulch Mine to learn the Bill Drill to actually break the rock inside the prison cell. At this point, Dilberta will run down the tunnel to Bullion Bill's hut. Follow her to get a jiggy in reward.