The Mac I recently bought doesn't really like me. At first it was just problems with it switching off sometimes (read - really often) or just showing the grey box of death on the screen, but yesterday it really crossed the line. It was sleeping quietly all afternoon and I decided to switch it off by pressing the socket button and today it just won't start. I tried the keyboard+power button combos, resetting the PMU button and nothing. What's funnier when I press the power button it lights up but nothing really happens and it dies when I stop pressing it (the light I mean).

Is it really dead or is there hope