I was working with that and forgot to plugin it in to charge .... When I plugin the power adapter the led near power connector of laptop is lit and the power button keeps blinking continuously in white colour.
Given your tests, it appears that either the battery or the charging circuit has failed.
The only practical action at this point is to have the machine serviced to determine what the problem is.
If uneconomical to repair, and since the computer is about 5 years old, then it may be appropriate to replace it now.