System completely Dead wouldn't boot

To start off you need to work this out carefully as its to soon to tell what is failing. Its best to work from the basic things then test the deep issues here as you don't have any clear symptoms that point to a HD issue.

On the side of system is a small button for the battery tester when you press it do you get any lights and how many?

What is the charger you are using? Look at the side the plug/cable is located on and read off the wattage. Sadly the print is a very light grey on the white body so its hard to read (you may need good lighting and a magnifying glass to see read it).

Have you tried a second known good charger? And are they both Apple original equipment units or some third party units?

Do you get your system wet at any point? Are you the original owner or did you buy this system used? Was the system ever serviced before? If so what was repaired.