I have the same problem: shortly after power-up the pc turns itself off. This happens regardless of what the pc is doing: booting, in BIOS, or just waiting at the GRUB boot prompt.
I notice that I cannot hear any ventilator fan noise whereas previously this was audible for at least a short while.
This is not the first time I have had this problem: previously I took it back to the shop and sent it away for repair. When the pc cam back from repair, it worked, I could hear the fan and I was told that they had changed the BIOS. It seemed unlikey to me that this was the only change since the PC did not stay powered on for long enough to perfom an upgrade.
Anyway, now the PC is no longer under warranty, I will try to find a replacement fan and install it myself.