Battery doesn't charge. (Inspiron 8600)

Okay, here's the history:

 

Started about a month ago.  First I noticed that the battery icon in my toolbar would switch between charging, not charging, and on AC power.  It got more and more frequent and my battery life was short when not charging.  Battery was about 2 and a half years old, so I thought it just needed replacing.  Finally did replace it (arrived just four days ago), and when I put it in, and then plugged the charger in, it didn't charge or go to AC power--nothing.  Then I thought my charger must be faulty.  I used the dell chat feature and went through some trouble-shooting and they finally just said they'd replace my charger.  The new one arrived two days ago and when I plugged it in, nothing.  I used the dell chat feature again, but in the middle of the conversation, it suddenly began charging.  The tech person said it was just a loose connection (which I didn't really believe since nothing had moved since first plugging it in) and the problem was solved.  It kept charging, but then when I moved to a different room and plugged it in again, nothing happened...again, and that's how it's stayed. 

 

Now the question:

An engineer where I work said it sounds like my motherboard is going bad, does that sound right?  I've already been through the trouble-shooting (powering up with charger/no battery-didn't work, with battery/no charger-did work, checking for damage at the ports/etc, replacing parts-brand new battery and AC adapter), and I really don't know what else it could be.  Help would be great.

Thanks

P.S.  Does anyone know (if it is a bad motherboard) if a motherboard will be replaced for free if the computer is still under warranty?