Computer does not starts, although graphic card's fan runs

Specs:
Gigabyte P35 DS3 rev.2
Core 2 Duo E6420
DDR II 2 x 1GB BallistiX 5300
8800 GTS 512MB
2 x Seagate 500GB SATA (7200.10 and 7200.11)

On the config (listed above), I see this machine starts itself daily at set times (via the bios), mostly do not worry. Some days when I arrive at the office, the machine has not started but the fan on the graphics card (8800 GTS) is running at full speed. As far as the machine concerned, it does not suffer any problem. When it actually started (it runs +/- 16H : 24H).

Please help to solve this problem.

I also had problems with cold boot on my old Gigabyte P35-DS3R. This was due to a DDR voltage too low when the motherboard started cold. The problem was solved by changing the batteries (of a lower voltage to operate normally). One thing that I found was to use the eve suspend to RAM rather than the extinction of the machine. So RAM continues to be fueled even with the machine stopped, and the floor of feeding the DDR remained at safe temperatures.

I have at least two opportunities to test to see if this is the case with me. I will begin by making the test suspend to RAM

In the Bios, it is called the "S3 Suspend".

But bios was already set to S3. In fact in memory, I tested this mode to see if it boot faster and had probably had to leave. I returned to see how S1 (without real hope therefore) if it would have an impact, but still the same symptoms. Anyways I tried using some different motherboard, and so the problem is solved. I think the motherboard was bad.

Anyways, thanks for your concern.