The A/C, installed or removed, will not prevent the car from starting. And, you don't need to cap the WIRES, you need to cap the evaporator lines running through the fire wall.
Have you tried to dis-arm the alarm yet? Lock then unlock the car from the passenger side, then see if it starts. The arm/dis-arm switch is on the door lock cylinders. The driver's side wears out or fails faster than the passenger side due to use. If that doesn't work, you'll need to trace the wires from the starter back to the relay. The alarm on the Supra's ungrounds the relay when the alarm is triggered. Resetting the alarm with the door lock usually resets the alarm and allows the car to start.
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