ASPIRE R3-131T doesn't get charged correctly

I noticed about 4 weeks back that my almost new (hardly used) laptop - model# R3-131T-P3BM.

Following are the symptoms.

1. Unable to Charge directly, have to shutdown the laptop or put it in sleep mode and then connect the adapater, after a while the charging light indicator turns ON indicating charging
2. When I see Blue light indicating the it's Fully charged, I start using the laptop again and when I unplug the adapter, I still see the "Charging" indication in the notification center in the main screen as if the adapter is still connected.
3. When I notice that the charge is low and connect the adapter for charging it sometimes shows the charging indication in notification center and sometimes doesn't. It is Random.

Initially I thought it's the adapter problem and called support to get some assistnace with the adapter.But now I think it's more to do with the Battery Pack or some hardware/driver supporting the charging function which isn't functioning correctly.