Originally Posted by
DualSportDad
the ability to shift out of park is not going to be hindered by fluid level. if i recall the shift assembly receives a direct input from the brake switch to energize the park release solenoid. this does sound like the OP has a bad shifter, either way i'd check for the ability to communicate with it with a scan tool, if not then i'd check power, ground and bus voltages and resistance to diag the issue properly.
I respectfully bow to Alex's experience / expertise / advice. I strongly suggest that you follow his recommendations . . .