You may have a faulty charger/battery or potentially a dead motherboard. To check if your charger is working, plug in the computer and see if it will turn on. If your computer still does not turn on, check to see if the light located on the charger is working. If there is not a light on, the charger may be dead. Consider buying a replacement charger. If the charger's light is turning on, plugged in, and the laptop is still not turning on, the mother board may not be working. Try looking over the trouble shooting page located at: Dell Inspiron M5110 Troubleshooting
Because the device is overheating, it is very likely that the fan on the device is broken or possibly too dusty to function. Sometimes, using the laptop on soft surfaces, can block the air path to the fan and cause the computer to over heat. However it is possible that the fan may be clogged or all together broken. One way to check this is to remove the fan and inspect it. If the fan appears dirty, try cleaning it with a clean cloth and replacing it. If the problem persists, then it is recommended that you replace the fan. Try checking out the Device Troubleshooting page for more additional help: Dell Inspiron M5110 Troubleshooting