Strange problem when turning ACER 1672WLMi on power

Hello, I for some time have a rather odd problem (and ****ting) with
my laptop ACER 1672WLMi. When it is on power, it works very well. If I
restart it, not of problem. Where that wedges, it is if I halt it,
and that I want to power it on a little bit later: impossible. At the
beginning, I awaited 5 or 10 minutes and that set out again. Now, it
takes him several hours of "recovery" (sometimes more than one night)
before agreeing to start again. Each time it's the same process: when
I press on the button "Power", the ventilator starts to turn in a weak
way during a few seconds (even not at all), and the computer halts
before starting. I don't understand, is it a problem of heating? (I
doubt sometimes that in 5 hours it do not have time to cool...). I
insist on the fact that once started the computer works perfectly
(never of restarting or undesirable cut). Did somebody already have
this problem?

Additional informations:
- that does not come from the alimentation (I tested some another);
- the problem comes with or without the battery;
- operating system: linux.

Thank you in advance!
Pascal