03 Grand Caravan Stalling with electrical loss randomly

I'm desperate. I've searched all over and haven't found anything helpful. I'm hoping someone here can help.
My wife's '03 Grand Caravan SE, 3.3 V6, has taken to stalling randomly. When it happens, all electrical power is lost as well; absolutely no lights, sounds, etc. Most times, it can be restarted right away, but the rest of the time, it has to sit for 30 minutes or so.
Tonight it happened on her way to work so I went out there to take her the rest of the way. In messing with it, I noticed that if I put the key in, the "door ajar" lite on the dash tried to come on, but was very flickery. I'm going to take it to autozone and see if they find any codes on it. I'll also try to really clean the terminals on the battery to see if that helps at all. I'll have her use my van key just in case it's that PassKey security system and maybe a problem with that.
Has anyone seen this anywhere else? Being an internittent problem, I know it's useless to take it to a mechanic. If they can't replicate it, they can't fix it, and I'll still get charged for them to look at it.
Please help me if you can. Without giving anyone a sob story, I'm in dire straights and I can't afford to lose the van too. Any advice would be GREATLY appreciated.

Thanks.

Battery/connections/cables/grounds are a good place to start. Bat cables are known to corrode internally without any visible evidence. Try shaking them and see if the power comes and goes. A trip to Autozone for a free code check and battery load test would be a good move.

There is a TSB out for 03s for no start/stall situations. It involves changing the Powertrain Control Module (PCM). May or may not apply. ID # 18-005-04 dated 3 Feb 2004. Also not sure if this applies to 03s but there may be a federal emissions warranty* of 8 years or 80K miles on the PCM. Check with your local dealership.

If you're not aware TSB stands for Technical Service Bulletin. These are "in house" Chrysler advisories sent to dealerships to help them with specific problems. Usually if your van is under a warranty Chrysler foots the bill for the repair. If not then you pay*.

I took it to get it scanned and since it doesn't have a check engine light on, nothing showed up.
I cleaned up the terminals really good and then tried it again. This time it shut off, same thing. Except the positive battery cable got REALLY hot and melted through the insulation. Any ideas? I'm going to go out and see if I can find out where everything goes, but I was hoping that this may be familiar to somone and maybe get some more ideas.
Thanks

Sounds like a bad battery cable was your problem, probably due to internal corrosion. It finally got bad enough to melt due to high resistance and show you where it is. Replace cable.