Very similar problems. Electrical failures for many years where the dealership has done everything from replace the battery (several times), alternator, disconnected Lo-Jack system, replaced transmission (yes, they said the electrical system in the transmission was causing the failures). Car is now out of warranty, and even Chrysler wants nothing to do with it.
Typically, one or more dashboard icons will illuminate. The car will start to lose power, and it becomes difficult for the electric window to close (no it's not the motor -- they've been replaced too!). The mechanics all want to go to the particular icon that is lit, or start by replacing the battery.
Finally, the last time I was at a new (different) dealership (original dealer won't look at it anymore) and they did all the same old stuff, down to replacing the battery. As I was leaving the shop, the battery icon came on and I made them test it as I watched. During several start-ups and shutdowns, the dashboard started lighting up like a pinball machine. They tested at the battery posts and watched as the voltage dropped from 13.9 to just over 5. It's not the alternator or the battery, but apparently some major power draw that intermitently happens. This virtually drains the battery to zero, where often it won't even charge unless you do a full overnight. There is some wiring issue in these cars, and since I've read two very similar problems on this site, has anyone encountered these issues and had them corrected?