That is a power-saving feature to conserve battery charge.
Sounds like you have a good battery. Is the battery plugged in when you try to connect with the cord? Does your battery charge when the cable is plugged in? If not, you may need a new power cable. Use a VOM (VOLT OHM METER) on it and do a continuity check to ensure connection is good. If that's not the problem, it may be the DC Plugin port.