What are the probable causes of DTCs P0352 and P1684?

It may run fine but it's in fail safe mode
DTC P0351-P0354
DTCs P0351 through P0354 Ignition Coil Primary/Secondary Feedback Circuit diagnostic monitors the primary circuitry of individual ignition coils for the successful completion of an ignition event. The ignition trigger signal and ignition fail-safe input signal provide crucial information in the control of ignition system timing and the activation of the fail-safe function. Based on the initial timing angle, calculated from the crankshaft and the camshaft position signals, the powertrain control module (PCM) calculates the ignition trigger signal. The ignition trigger signal is then sent to the ignition control circuitry located in each ignition coil. The ignition control circuitry initiates the ignition dwell period by commanding the power transistor ON. When the PCM determines the proper time to provide spark, the PCM turns OFF the ignition trigger signal. In response to the PCM signal, the ignition coil control circuitry turns OFF the power transistor, producing a high voltage discharge from the secondary coil windings. After the spark has occurred, the control circuitry sends an ignition fail-safe input signal back to the PCM, confirming that an ignition event has taken place. If the ignition fail-safe input signal is not received by the PCM, a cylinder specific DTC will set.
Anytime the fail-safe input signal is lost, engine operation will enter the fail-safe function. If engine load exceeds certain parameters during the fail-safe function, Fuel Cut-off mode is activated and fuel injector operation is ceased. The suspension of fuel injection in the Fuel Cut-off mode protects the catalytic converter from damage. Damage can occur when excess unburned fuel reaches the converter and causes the catalyst to overheat.

Diagnostic Aids
• Check for the following conditions:
- An interruption of the ground circuit or voltage supply to the ignition coil will prevent a proper ignition event from taking place. A DTC P0351 through P0354 will set if there is a fault in any of the ignition coil circuits.
- If DTCs P0352, P0353, and P0354 are present, the fault is located in the shared electrical circuits or shared components of the ignition coils.
- Inspect the ignition coil grounds at G 105 for a clean and tight connection.
- The scan tool data parameters for Misfire Current Cylinder # are frozen at the time the MIL illuminates when the DTC sets.
- If no engine misfire is felt when the DTC sets, inspect for a fault in the Ignition Fail-Safe Input circuit.
- Inspect the noise filter for an internal short or low resistance. The ignition coil may not receive adequate voltage during high load conditions if the noise filter is faulty. A good noise filter will indicate infinite resistance (OL) with a DMM after the capacitor inside the filter is charged up.
- Unless the ignition key is cycled or the DTCs are cleared, the PCM waits to receive ignition fail-safe signals before providing fuel injector operation.
• An intermittent malfunction may be caused by a fault in the ignition coil electrical circuit. Inspect the wiring harness and the components for an intermittent condition. Refer to Intermittent Conditions .
• Repair any electrical circuit faults that were found. Refer to Wiring Repairs .
• The information included in the Freeze Frame data can be useful in determining the vehicle operating conditions when the DTC first set.

2004 Dodge Ram Truck 1500 2500 3500 Service Repair Manual INSTANT DOWNLOAD

for the easy solution download the pdf file

It's not the coils . It's the PCM , transistors (driver) inside the PCM are fried .
P0352 Ignition Coil B Primary/Secondary Circuit Malfunction

P1684 Dodge Battery Power To Module Disconnected

https://www.autocodes.com/p0645_dodge.html

check engine light on means one or more DTCs are stored in the engine control model.
maxiscan us703 can help you clear the fault codes.

P0300 code is random misfire, P0352 code is ignition coil be wire malfunction, P0352 that the main problem If you are equipt with COP (coil on Plug) one of the are disconnected or at the harness to the ignition coil.

If the vehicle runs fine other than the P1684 code then it is probably the result of the battery being disconnected sometime in the recent past.
Hope this helps.

302 is misfire on cylinder 2. Please see my tip at http://www.fixya.com/cars/r6715318-causes_gasoline_engine_misfires .
1684 is battery disconnected, which you caused when you disconnected it--you can ignore that. You probably have an intermittent misfire. Please follow my troubleshooting steps and let me know if you have questions.

Maybe it is problem with fuel, or fuel filter or pump…. Try with Diagnostic Trouble Codes (DTC)

1. Cycle the ignition key On – Off – On – Off – On within 5 seconds.
2. The Odometer will show the P-Code for the DTC code number. (send me a code if you don’t have chart with DCT’s)
3. If no DTC’s present, the cluster will display one of two texts: “P1684” and “done” or only “done” .
1. “P1684” is only a status and indicates that the PCM memory has been cleared within the last 50 ignition cycles and does not indicate a problem
2. “done” indicate that no DTCs are present and the procedure is complete.

P0340
Camshaft position sensor circuit

• Most likely cause : Camshaft position sensor failed.

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P1684
means the battery was disconnected(or had been drained to a low voltage) recently.