The improper shutdown (dunno really the right words here... i understand english very well but writing and speaking...)
i have no problem understanding you

the comment about improper shutdown was a joke.
Hmm i need to check what chipset is on this laptop... (Can i see this in Windows or do i look for the printed manual?EDIT nothing in manual, didn't find anything in Windows, when i restart this, i'll check BIOS..)
my guess would be that it's something from the intel 900 series. a few of the models there were optimized for low power usage. i highly doubt it's an nvidia chipset, and i can't imagine it being a 780i. i only mentioned that as an example. intel chipsets are pretty good in general, but there's no accounting for the occasional defect.
i hope we didn't make mistake when when we threw the large box to dumbster...
most of the time OEM (original equipment manufacturers) print the serial numbers their support teams will need directly onto the product. there's a good chance there's a label somewhere on your laptop itself.
good luck with Asus! i myself have a bad pattern of not having problems with things until the day after the warranty runs out