Call it in to HP, because what you're describing are hardware failures. While purely my opinion, even if I do think it's clearly supported by ample anecdotal evidence on this forum and others like it... HP systems are crap. They are pretty to look at, but where it counts, they are complete and total garbage. If you look at this forum, and other forums across the Internet, I think you will find that HP/Compaq and Acer/Gateway/eMachines (they're all only two companies now) make up a disproportionate number of complaints by people.
In any case, with WinNT/2000/XP/Vista/7, the only time you should be seeing BSODs is if there is a hardware failure. Since the system is only a month old, it's still under warranty, thus you should be making this HP's problem to fix. Sounds like you have a bad video card/chipset, which will almost certainly mean motherboard replacement. Call HP, and don't hang up until you have a date and time when they will be sending a tech by to fix your system, or that they will be sending you a box to mail your system in for repairs, with a paid shipping label. You could also probably try to declare the laptop a lemon and simply have them send you a replacement. However without them attempting at least SOME troubleshooting, that's an unlikely scenario.
This HP Pavilion dv4-1228-ca computer with Vista Home Premium on it has been a real test of patience!
We have only had this laptop for 1 month but today it really died, after many pink-stripped screens during these few weeks. I thought Windows ME was bad but my one month with Vista was worse. Windows 2000 and Windows XP are much easier to use, at least for me.
Today my pink-stripped screens disappeared but turned to blue screens.
Yes, I searched high and low for Vista help even on these forums but those frozen screens kept coming back whenever they wanted to at various times.
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