You said "I started the car for the first time and applied the brakes and the calipers locked up..." Did you try to drive the car at all? The piston is pushed back into the caliper by the minute wobble of the rotor when driving.
I'm assuming you have the floating caliper system with "ways" that locate the caliper on the spindle. Remove the brake pads and slide the caliper back and forth on the ways. It should slide without hanging up. Check the way for rust or nicks. If it hangs up, use a flat file for metal on the way. I prefer the flat file as it avoids creating peaks and valleys I might create with a grinding wheel.
