Latitude E6540 sudden shut-off 8 seconds after starting

I am using a Latitude E6540 as part of my university work. We have recently tried using the device again after a short hiatus (a few months) and are having an issue getting the laptop to start properly.

When the power button is pressed, the Storage 'Device Status LED' next to the power button lights up for 5 seconds, then disappears. 3 seconds later, it reappears briefly, there is an audible 'click' from the laptop, and the machine powers off completely. During this sequence no other lights on the computer (outside or inside) light up at all. The screen stays completely black throughout. 

So far we have simply tried purchasing a new power adapter - the issue is the same when this is plugged in to the machine. Any help will be much appreciated.