Screen goes blank and computer frozen at random times

Two days ago I downloaded and installed the game Minecraft for my son. After successful install, when I first opened the game my laptop screen went blank and no other response from it (well not actually blank, but vertical black and white lines). I had to press and hold the power button to shut it down, and then tried to turn it back on. The fan and lights came on, but no response from the display, except the backlight. Not even the bios splash screen. I shut it back down and let it sit for a little while and tried to boot again and this time was successful just as if nothing had happened. Everything seemed to be fine except it was now running a little sluggish. I proceeded to uninstall the game and ran a full virus scan with Malware Bites Anti-Malware, which found nothing. I then figured it was just some type of glitch or overheat and played around with it for a little bit and everything was working fine. I then walked away from it, but just by chance happen to notice that as soon as the screen saver came on I had the same blank screen and frozen problem as described before. I shut it down as I did before and tried to restart, but this time it restarted just fine (as opposed to the last time where I couldn’t even get the bios “flash screen”), I only booted into safe mode this time. Again, everything seemed fine while in safe mode, so I took a break and went to have dinner only to come back to another blank screen remembering this was while it was still in safe mode. I rebooted again into normal mode and ran system restore to the day before I installed the game. After the restore I played around with it more, tested the screen saver, played some videos, etc and it seemed fine, except for still the sluggishness. I walked away for a little bit glancing over every now and then to see if it happened again and I saw the screen saver working just fine. Then just randomly it happened again; blank screen and un-responsive. I can’t seem to see anything in specific that triggers it.
It has happened a dozen more times intermittently since then and seems to have no rhyme or reason to what causes this problem. Sometimes the screen goes completely blank, other times it has those vertical black and white lines, sometimes it restarts just fine while others I can’t even get the bios screen/pre-boot info to display, and others I get the bios to display, but stays blank afterwards.
In my own research and knowledge it may seem like a hardware problem, but if it is indeed something like the graphics adapter failing, would it not be just a working or not state? Why would it work sometimes and then fail after a random amount of time working. Another suggestion would be some type of overheating problem. I have had problems with the fan screaming and bottom of the laptop very hot, even when the computer is at idle, but through this whole problem the fan has been nice and quiet and I have even taken more precaution and given the bottom vents more ventilation. Being that most likely it is probably related to one of those suggestions, I still find it a little too coincidental that the problem started just as the graphics loaded when I first started that game mentioned in the beginning.
Any suggestions? It is really getting annoying… I think it’s fixed or it’s not showing symptoms then I’ll walk away to come back to it frozen. Just an added note, with the exception of one time (not including the original event) every time it freezes/goes blank it has been while the computer is at idle with nobody using it.

Thanks for the suggestion. i am not really having a problem booting windows, its just that whenever my computer "crashes" sometimes i just have to wait about 5 minutes (maybe for it to cool???) before it lets me (meaning the screen will display windows booting), nor do I have any problem getting into safe mode. I did, just to be safe, go through that checklist anyway and everything seemed ok. I also updated the display driver from the HP website. I dont want to say its working fine now, but the events are far and few between. Before it was anywhere between 15 and 30 minutes after startup before it randomly crashed, and now it has crashed only three times in the last 5 or so hours.

If I try to update my Windows Experience Index, it will instantly crash as it was doing before, but (so far) if I just leave it on and walk away, its still ok whenever I return. Its not like I always need to check and update my Experience Index, and if that is the only thing that is making my computer crash, i can live with it, but I fear that if that is one trigger for the crash, what else is there that I haven't opened yet that will trigger it? Now that it's not such a random occurence is there any other suggestions on to what is causing this problem and how to fix it?

I will run memtest overnight tonight and post the results when finished.

In addition to working through the Troubleshooting Steps to gather clues, I'd post up in our Crashes forum the Blue Screen of Death (BSOD) Posting Instructions for expert analysis which may narrow it down to the exact cause for you.

Ok will do, but I never actually got the BSOD. Maybe I was using the term crash in the wrong mannor. what I meant by crash is that the screen will go black or have vertical white stripes and no response from the computer in any other way. see the attached image

Can you plug in an external monitor (to most laptops) to see what appears?

If that works uninstall and reinstall your Display driver, check for an Update via optional Windows Updates and your model's Support Downloads webpage.

I already updated the graphics driver to the latest version prior to posting here. An update on the situation...

Last night I was using it for about 3 hours straight, just doing random things like cleaning and organizing folders and what not (nothing too graphic intensive), hoping that it would "crash" while using it so I would know a trigger, but it was working perfectly while using it. i went to bed and came to it this morning and of course, blank screen and unresponsive. After a hard shut down and reboot, everything seemed fine as usual but my desktop background was all black (icons and locations the same). In the personalization panel, it stated that it should be the image I previously had, but wasn't displaying it. I unchecked the image and rechecked it and it displayed just fine again. Its no big deal, but was thinking this may be some type of indication as to further diagnose this problem I am having.

I took it to work to connect it to my work monitor and at first everything seemed ok, but as mentioned in an earlier post, a trigger to make it "crash" was to update my Experience Index/System Rating. Unfortunately while connected to an external monitor, it still crashed when doing so.

With the exception of the system rating trigger, it only seems to happen while the computer is at idle for a certain amount of time.

Any other suggestions???

I'm guessing this is most likely your Display adapter, either its driver or the chip itself becoming loose or going bad. Someone else might have a different idea.

Try every driver available from Vista forward. Remember the drivers W In7 wants are delivered via optional Windows Updates when you enable Automatically get recommended drivers and updates for your hardware.

Try different screen resolutions and refresh rates.

Try running both with and without the driver software package checked in msconfig>Startup and >Services. The Catalyst bloatware can be a problem sometimes.