If my experience with Dell is anything to go by, you shouldn't have any trouble getting your laptop repaired, although I think in your case I'd be asking for a replacement as things have gone pear-shaped a week after you bought it.
Anyway, back to my experience. I bought a Dell desktop in May 2010 through my local reseller and a two-year guarantee was included in the deal.
The motherboard failed a couple of weeks ago so I took the tower in for repair expecting to be without the computer for at least two weeks, so I was surprised to receive a phone call the next day telling me my computer was ready for collection.
It turns out that Dell franchise a lot of their repairs to agents around the country. When the one for my area was informed of my predicament she arranged to call into the store the same day to see if she could do the repair.
One motherboard, one CPU, one heatsink and three hours later, my computer was as good as new.
I'll keep my fingers crossed that your outcome is as good.