Ignition coil shorting out 2 minutes after starting car

The hot coil is what happens if you plut a battery across it for more than a few minutes.
Replace the damaged coil and check for a spark. If no spark, check the points gap and condeser.
Never leave the ignition on for more than a minute without the engine running, it damages the coil!

Direct Ignition cylinder ignition system that ignites one cylinder with one coil.
Possible causes.
Ignition Coil No. 3
Ignition Coil No. 3 harness is open or shorted
Ignition Coil No. 3 circuit poor electrical connection
Possible bad ECM, Electronic Control Module

P0351 loss of power ? That's not what this code is about . P0351 - Ignition Coil A Primary/Secondary Circuit ,you have a bad coil and possibly a bad coil driver inside the PCM . Do yourself a favor an take your vehicle to a qualified repair shop !
P0351 - Ignition Coil A Primary/Secondary Circuit Description: See the description for DTC P0350. Possible Causes: See the possible causes for DTC P0350. Diagnostic Aids: See the diagnostic aids for DTC P0350. Application Key On Engine Off Key On Engine Running Continuous Memory Coil-on-plug (COP) ignition testing - GO to Pinpoint Test JF . GO to Pinpoint Test JF . Coil pack ignition testing - GO to Pinpoint Test JE . GO to Pinpoint Test JE .
P0350 - Ignition Coil Primary/Secondary Circuit Description: Each ignition primary circuit is continuously monitored. The test fails when the powertrain control module (PCM) does not receive a valid ignition diagnostic monitor (IDM) pulse signal from the ignition module (integrated in the PCM). Possible Causes:

• Open or short in the ignition START/RUN circuit
• Open coil driver circuit
• Coil driver circuit short to ground
• Damaged coil
• Coil driver circuit short to VPWR

Diagnostic Aids: Use the 12-volt non-powered test lamp to verify START/RUN voltage at the ignition coil harness connector.
Check the coil driver circuit for open, short to VPWR, or short to ground. Application Key On Engine Off Key On Engine Running Continuous Memory All GO to Pinpoint Test JE .

Coils can short only due to short in the wires, Spark plug or Ignition Module. Please read this article for better understanding the Coil issue.
www.aa1car.com/library/ignition_coils.htm

The P0302 code means that the cylinder 2 is misfiring or is randomly misfiring. Start by checking for intake leaks an if no leaks are found the next step is to replace the spark plugs on cylinder 2. If the problem persist more tests needs to be done to diagnose problem, see "Possible Causes"
- Faulty spark plug 2
- Clogged or faulty fuel injector 2
- Faulty ignition coil 2
- Fuel injector 2 harness is open or shorted
- Fuel injector 2 circuit poor electrical connection
- Ignition coil 2 harness is open or shorted
- Ignition coil 2 circuit poor electrical connection
- Insufficient cylinder 2 compression
- Incorrect fuel pressure
- Intake air leak

more than likely your spark plugs they should be changed every 60,000km

p0685 refers to ECM power relay control---circuit open===causes--wiring--ECM relay
Replace this relay. Check the wiring from the coil to the distributor as there is a dead short after the coil somewhere for the fuse to blow and the coil to overheat.. You may have a electronic module failure either in the distributor or the ECM

Symptom table:
- Open or short in Ignition confirmation signal IGF and Ignition Trigger signal IGT1 - IGT2 - IGT3 - IGT4 from Ignition coil to igniter.
- No.1 - No. 4 Ignition coil with Igniter.
- Engine ECU.

To find the missing problem do the following:
- Spark plug No. 2 short or defective. (replace).
- Open or short in Ignition confirmation signal IGF1 or Ignition trigger signal IGT circuit between ignition coil with igniter and ECM
- No. 2 ignition coil with igniter. (replace with good known one)
- ECM. (replace with good known one)

I suggest you check base timing ,timing belt wear or missing teeth on timing belt or short in ignition circuit

Sounds like ignition control module (small plastic piece in bottom of distributor). When it gets warm it's shorting out. Easy fix, disconnect battery, pull cap & rotor - gin module is 2 screws in bottom of distributor and 4 wires - replace wires in exact order and coat bottom of middle with dielectric grease, replace rotor, cap & connect battery NEGATIVE CABLE LAST!