In The Family of Blood, the Doctor uses the chameleon arch to turn himself human. It is a cloak to hide his Timelord self from the family. The circuit is what makes the TARDIS the blue box. My question: are the chameleon circuit and chameleon arch connected, and if so, why did it turn him human if the circuit is broken? Please, a cannon answer.
No, the Sixth Doctor episode Attack of the Cybermen from 1985 showed the Doctor attempting to fix the chameleon circuit (causing the TARDIS to assume shapes other than a police box, though still malfunctioning since the shapes didn't serve the purpose of camouflage), and all he did was open a panel in the wall and mess with some electronics inside, as shown in image st--6t01.jpg from this page:
The idea of the chameleon arch that could change a Time Lord's biology wasn't introduced until the 2007 Tenth Doctor episode Human Nature, and it was never suggested that it was connected to the chameleon circuit. Maybe the Time Lords just like the prefix "chameleon" for a device that disguises something's true nature.