Battery Causing Laptop to Crash???

I have a Dell Inspiron 6400 that just randomly freezes.  I get a black screen.  The power is still on, but there's nothing on the screen.  Sometimes I am able to use the laptop for several hours before this happens while other times it happens after just a few minutes.  I have been trouble shooting this for two weeks now.   My first thought was that the LCD was bad so I hooked up an external monitor and waited for the next crash.  I lost the screen on both which rules out the actual screen.  At this point I also noticed that the laptop was freezing or hanging because the the caps and num lock keys were not engaging.

I next upgraded the BIOS to the lastest version and this did not help either.

I ran a virus/malware scan and everything came up clean.

I then ran Memtest on the memory for a while and everything came up perfect.

At this point, I'm thinking that it is completely hardware based, perhaps the motherboard being dead.  I own two of these laptops.  The other is almost identical except for maybe on or two components.  So I started swapping components in order to eliminate things.  The first thing I swapped was the Hard drive since almost all of the drivers are identical.  This was a huge step.  I still had the problem on the same laptop which told me that it's not software related.

As mentioned above I had already run a memtest on the memory, but I decided to swap the memory just to double check.  Still had the problem on the same computer.  At this point I am totally thinking it's a bad motherboard.

I treid swapping the power suuplies and still ended up with the same results.

I then deicded to swap batteries,  Neither of the batteries hold a full charge anymore.  I alkways use these computers plugged in and although many manufactureres recommend that you take out the batteries when using the computers plugged in for a long period, I do not because the battery actually act as a UPS if ther happens to be a power failure.  The battery on the problematic laptop holds a 3 minute charge and the battery on the good laptopn holds a 20 minute charge.  Since swapping these batteries, I have not had a crash on the problematic laptop.  I havent had a crash on the good laptop either, but haven't been using it either.  It's just sitting there with XP loaded and plugged in.  It's been about 12 hours now.  I'm hoping to get a crash on the "good" laptop so that I know for sure it was the batery causing the issue.

If the battery is indeed the problem, it doesn't make sense to me.  My only thoughts are that perhaps there is a powering problem with the motherboad where there is just a slight instaneous loss of power on the plug side of the motheboard and the worse of the two batteries is not strong enought to keep the laptop going?  But this wouldn't make much sense either seeing that this bad battery holds a charge on the good laptop for aprox 3 minutes.  Could the worse fo the two batteries just be creating the crash period and there being no problem on the motherboard side at all?  I dont get it.