Laptop Battery

Dell Inspiron 4000 works fine with AC Adapter connected. No over heating, no problem and Power Options says battery fully charged. When laptop is then powered on for about 10 minutes without AC Adapter connected, laptop gives shut down message, case bottom is very hot and Power Options says battery is less than 1%. What is causing battery to drain from 100% to 1% in 10 minutes while unit is overheating? Fan was just replaced and problem still exists.