So, if I push in the parking brake to set it I get a buzzing sound and the red Brake error light shows up on the dash, and the parking break will not engage.

I haven't unpacked my ramps yet, so I haven't been under the car yet in a safe manner. Should I be expecting a broken cable?

Or your cable isn't adjusted correctly or your brakes are so worn or out of adjustment.

The rear drums are shot, I'm hoping as soon as I get in there for the brake job, things will be better.