Could be your battery. Check the battery connections and give them a clean. In some laptops you need a battery in place even if it is dud and requires a mains adaptor.
Also, as you point out, it's getting hot. So the cooler fan may not be operating to full capacity (if at all). Could be due to dust.
Have you always used the laptop on a flat surface with plenty of ventilation (i.e; as a desktop replacement)?