you mentioned security light blinking
1- If the light is blinking while key in ignition or while you trying to start it that means security alarm is on ,no power to starter and no fuel pump operation .
2- If that is the case most likely the dead battery triggered the alarm ,we can try to reset it ,as long as no issue with alarm components
3- You also mentioned a screeching sound noise , that worries me , Because if the ignition switch is bad , it will also trigger the alarm ? i will need more info from you on that
4- The after market key fob is a separate keyless Fob is for the lock / unlock feature correct , you have a separate key for ignition correct ,Not a key/fob into one ?
Security light should blink for few seconds and Go Out ( OFF) completely after you insert the key in ignition switch , If not the Alarm is ON causing the No crank Condition
please let me know so I can further assist you
Chad ( aka Customer)