It's definately a battery problem. When you exchanged your mini, they most likely put your old, bad battery into the new unit. I received a Mini 9 on the Dec 25 and on Dec 27 the battery was not charging. I spoke to Dell support and before I could even get the issue out, they told me it was the battery and they will send me a new one.
I'm running XP; however, it looks like the folks running the unix version are able to fix the issue via a software setting. I've tried everything (updated BIOs to A03, tried the Fn-B boot sequence, shook the battery, etc..). Now the battery has no charge and the two LEDs on the front are alternating flashes. My new battery should be here by Wednesday.