The diagnostic and tool options suggested already are fantastic, and you should seriously consider one of two options.
Follow the advice you have been given and use the tools suggested to attempt to uncover the reasons for your crashes.
Send the computer back to the manufacturer to be checked.
From the content of your question, and the lack of pertinent information, I am not sure that Option One will be the one for you. You see, this problem has been going on for 8 months now (June 2011 was 10 months ago, and the problems started 2 months after getting the machine) and you have not come to the realization that fixing it is beyond your capabilities. I'm not saying you cannot replace a bad video card or stick of Ram yourself. What I AM saying is that you do not appear capable of diagnosing and determining exactly what hardware is bad if you have not been able to do so in 8 months. Yes, there is some credit due to you for finally asking for help, but based on how long it took you to ask I do not believe that it will be of much use.
For example. Did you know that you can write down the code from the Blue Screen error, and then search for it at Microsoft Support? That's right. If you were getting an 0x0f4... or rather an 0x000000F4 error... or if it looks better a STOP: 0x000000F4 (0x00000003, 0x8293CDA0, 0x8293CF14, 0x805C773E) error, Microsoft can tell you what the most likely cause of this error is. That's what BlueScreenView is for, and why it was suggested to you. However, this diagnostic tool is not going to fix anything. It is only going to help you identify the issue, and it will still require work on your part to do even that.
Since you suspect this may be a serious hardware problem, you are most likely better off putting it in the hands of the manufacturer (the company that assembled the PC) and letting them determine what the issue is. You can keep the monitor at home though. They won't need you to ship that back to them.