My S5i will not turn on with battery power

Served me well for years. Was in case in car [avg tempt 40-50degrees for a week.] No response to on button. Using Pentax external power supply, turned right on and first screen was white screen asking for time and date set. Set that and..... with power supply, takes, stores, plays back pics fine. Both my batteries are fully charged.....camera not sensing the power? Contact issue? Other? Made sure contacts were clean....any suggestions? Note: love this camera but it does not owe me anything. Ron