Need help with my Inspiron 8100!!

It starts up and runs fine on AC power, and runs fine on batteries if the AC connection is removed while powered up, but will NOT power on if the AC connector is not plugged in.

I've tried replacing the batteries, upgrading the BIOS, and replacing the battery charger/power board (starting to get expensive). Dell tech support was absolutely useless- after about 2 hours of phone support, the only solution they can come up with is to replace the motherboard (they want $700 for that!).

I'm wondering if the problem is in the BIOS settings or power management, but I haven't come up with anything so far. Any help would be greatly appreciated!