Q: 2008 Buick Enclave engine light on with code p1682 and car stays running with key off for while then dies, ECM is humming,

Code P1682 sets if the ECM detects a difference in the voltage levels of the two main power inputs to the ECM. Basically, the code will be stored when one voltage input has a significantly different value than the other one. Often a wiring faults, including corrosion on terminals, is at least a part cause. Other possibilities are a fault with the ignition switch itself or a fuse/relay in the circuit. You can start by inspecting the the power relay and start power relays; indeed, a fault there, in a relay, may explain the humming noise at the ECM. Based on what you are describing a mechanic can resolve this for you and so I recommend you request a diagnostic and the responding certified mechanic will get this taken care of for you. If you have further questions or concerns, do not hesitate to re-contact YourMechanic as we are always here to help you.