The battery won't charge with an unrecognized AC adapter.  If it's not OEM Dell, that's the issue.  If it is, either the adapter has failed -- or the DC input jack.  Try a new OEM adapter first.  If it is also unrecognized, replace the DC jack inside the system.  
Charger won't charge.  Charger ref is AA45NM131.  Diagnostic check says battery is okay, but charger 'unknown'.  The laptop operates when the charger is plugged in.  Adaptor part does get hot.
charger not charging laptop