P0300 is a random misfire on different cylinders (nothing specific).
however P1310 has quite narrow trouble are:
-Open or short in IGF or IGT circuit from igniter to ECM
-Ignition coil (No.2)
-ECM
the reason why your car shuts down is that once ECU looses signal (IGF or IGT) from coil no.2, it will go into fail-safe mode forcing the fuel cut condition. once the signal is restored (coil replaced or wiring/connector fixed), it won't do it again unless the ECU is faulty and causes the problem in first place.
first check the plug to ignition coil no.2 (IIRC it serves cylinders 2 & 3) for any obvious damage and at least visually check wiring for any damage spots.
would be good if you could check wiring continuity between coil and ECU end with an ohm-meter.
you will need electrical wiring diagrams to do that.
ultimately you may need to check the ignition coil, at least the resistance checks (primary and secondary circuit).
Autozone ignition coil check for 5s-fe:
Using an ohmmeter, measure the resistance between the high-tension terminals. It should be between 9.7-16.7 k-ohms when the coil is cold or 12.4-19.6 k-ohms when the ignition coil is hot.
http://www.autozone.com/autozone/rep...00c1528009242d
likely the coil went bad or wiring is damaged, ECUs do not go bad that often.
PM sent.