2000 Chrysler Town and Country has been running rough for some time. It doesn't do it all the time but lately it is happening more often. We replaced the coil pack and that didn't help. We took it to a mechanic and he replaced the computer today but that didn't work either. The error code was 3405. Any suggestions? It also backfires occasionally when I try to give it some gas especially if I'm on an incline or the air cond. is on.

SOURCE: town and country

CHECK FOR INLET MANIFOLD LEAKS OR EGR LEAKS..

SOURCE: error codes 442 and 456 on 2003 Chrysler Town and Country

Could be the gas cap.  Do you fill the tank with the engine running?
Otherwise, check the hoses near the Evap canister.  I have 2003 T&C and had the small leak and large leak codes.  I looked at the evap cansiter and the hose coming from the fuel tank vapor line had a huge crack in it, to the point it had fallen off the evap caniser.  I trimmed the end of the hose and reconnected and voila, no codes.
The evap canister is on the driver's side of the van, underneath, slightly behind the drivers seat.
BTW, to clear the codes without an OBDII reader, remove the negative cable for 5-10 minutes (15 to be safe).  The computer resets and clears the codes, except for one that it sets saying loss of power to the memory.

SOURCE: Ignition coil keeps busting open

YOU EITHER HAVE A COIL DRIVER CIRCUIT WIRE SHORTED OR FAULTY ENGINE CONTROLLER(PCM)..CHECK NEAR TRANS DIPSTICK FOR ANY DAMAGED/MISROUTED WIRING..HAVE SEEN IGNITION COIL DRIVER CIRCUIT PROBLEMS WITH PCM'S IN THESE VEHICLES ALSO

SOURCE: 1996 Chrysler Town & Country won't start

If you have fire, then it's probably a fuel problem. Turn the key to the on position, you should hear a 'whirring' sound from the gas tank, which is the fuel pump. This sound will only last a few seconds , but should indicate that the fuel pump is working. If no sound, check the fuel pump fuse, fuel pump relay, and the fuel pump itself . Good luck.

Testimonial: "Thank you so much for the offer of help. The pump is woking fine, in fact we replaced it about a year ago. I can hear it running."

SOURCE: van hesitates and sometimes backfires when

i would like to tell you to pull a spark plug and see what's going there....you may see a spark plug that's all burnt up or a different color then the rest..extremely different...due to either, pre-ignition or detonation...in that case replace the plugs, with the proper heat range spark plugs, i highly recommend a factory plug to avoid any issues with the heat range or anything else. If problem still persists, then it may be a fuel issue.. a system that is too lean, getting less fuel and more air, will cause a back fire, as the oxygen in your combustion chamber will ignite very quickly and stay lit through out the strokes and when the valve opens, it back fires..so try a tune up first because then you will know for sure if an injector is bad, whether its firing right, or not at all...if problem still persists, then have your mechanic perform a fuel pressure test and if there is a significant drop in pressure, could be regulator or pump...just to try cheap first? replace the fuel filter and air filter...it might be due to a lack of fuel reaching the engine..if all checks out well, then it could be a worn timing chain, or burnt valves, or timing chain