Precision 3240 Tower does not boot

I have a desktop Dell Precision 3420 Tower. It is presenting those behavior:

does not boots up;

does not turns on the keyboard  - the caps-lock led does not turn on or off afer pressing  Caps-Lock key 

does not show any image on the screen,  even using off-board or on-boad video adapter.

Also:

It keeps turning itself on. Just plug power cord on it and it turns on (no power button pressed is needed). By the way  , If I press the power button  for 5 (or even 20, 30, 35, 60...) it  does not able to keep itself turned off over 5 sec and turns on again.

Measures that I´ve already done:
I´ve Exchange the hard drive; memory modules (I exchanged the positions among them and put other ones, as the originals) ; video adpter (it was removed to use on-board adpter and back again).
So ... I´d need to know What path I must to follow to investigate and to know what is causing those problems?