My D620 has been doing odd things over the past month or so (screen
going blank), but it was always fixed with a reboot. However last week
the screen went blank and would not recover. On boot up the power light
would start, the hard disk light would flash and a second later it
would stop, no POST screen, no graphics nothing.
From your description alone it's just not possible to pin down what the exact problem.
My only guess would be some critical motherboard error. It could be CPU, RAM, graphic chip or any other key motherboard component.