Are you sure you plugged back in all the cables you pulled out from underneath the driver side steering wheel. i just did my heater core about a week ago and I didnt have that problem also did you remove the negative terminal off the battery before you proceeded to replace the heater core because that could of possibly been the culprit if you are absolutely certain you didn't miss any electric connectors. Another culprit could be that your shifter linkage go pulled back to much and its in gear and the car of course wont turn over unless its in park. I dunno those are really only the three things I can think of. Let me know if you figure it out or not.