My laptop won't switch on

My laptop is 14 months old, I was going through my emails on it today, and it cut to a blue screen error. I unfortunately didn't manage to get the error code, as the screen almost immediately started displaying pink stripes down it which continued to get worse.

I switched it off to prevent further damage. However, when I tried to switch it back on, the computer now won't boot up. It just shows a black screen, and the caps lock button blinks in a 5 slow 3 fast pattern.

Does anyone have any idea how I can try to fix this myself? I asked for a quote from HP and they said it would cost almost £500 to fix based on the same information here. Are they taking me for a ride? I don't have much money, and saving up for this laptop for my studies was a not so trivial task in itself... now having to pay for a repair for a "high end" laptop that should last considerably longer, when its only just out of warranty... it seems like such a scam.