I had an older Dell inspiron 15R that had similar issues where the AC adapter that came with the laptop was not recognized.

There was a problem with the adapter and possibly the power jack. There's a small ring that goes on the tip of the portion of the adapter that gets plugged into the machine; somewhere along the way, this ring went missing. I can still power the laptop with this adapter, but it's not recognized by the system. There was also one instance when I was connecting the adapter where it produced a nice blue spark and a small puff of smoke ... but, after waiting while, the adapter powered the machine normally, albeit with the "AC adapter not recognized" message.

I've since replaced both the adapter (with the ring intact) and also a new power jack within the laptop, and it works like new.

-PeterMac