Well I found that there is a cable between the ignition switch and the shifter, requiring that the brake be applied before the button will depress.
Is there a way to disable this cable? How difficult would it be to replace the cable?
Make sure your shift handle is fully seated on the shifter. That can prevent you from releasing the shifter.
The shifter interlock cable serves 2 functions -- it prevents you from removing the key without the shifter being in PARK, and keeps you from shifting out of PARK without pressing the brake pedal.
Replacing the shifter interlock cable does require dropping the steering column, and removing the center console. Not too difficult, but probably time-consuming.
If I were you, I'd just inspect the cable and look for damage -- especially at the ends. If you don't see any, I would suspect it's the brake-shift interlock. This system consists of a solenoid at the steering column end of the interlock cable, and the Brake On-Off (BOO) switch.
If you disconnect the wire that comes from the BOO switch at the solenoid and can move the shifter out of PARK, you probably have a bad BOO switch (they're usually plastic and can break easily). If you still can't move it, then you probably have a bad solenoid. Since the BOO also controls your brake lights, see if they are working, even though they could possibly still work with the interlock portion failed.
If you do disable the interlock solenoid, get the problem fixed as soon as practical. The interlock is a safety device.