Memory_Management, BSOD

Just bought a computer last year (May 2011) and more than a year later this happens to me if a program uses to much memory I think. I run it 8-10 hours on May 2011 to February 2012 ,9-12 hours during summer (March-June 2012) and after that 7-10 hours on week ends (June to Oct. 2012). Before it BSOD it somewhat warns me like programs not responding like google chrome has crashed, sidebar.exe not responding, windows media player not responding. I also don't have a history of overheating. I do not have a recovery disk.
My Specs are:
Pentium Dual Core CPU E6700 @ 3.20 GHz
Intel G41 Express Chipset
2.00 GB RAM (Samsung 2rx8 PC3 10600u)
DirectX 11
Windows 7 Home Basic 32-bit
BIOS Date: 08/12/10 11:36:37 Ver: 6.05

This is the rest of my BSOD's:

Your dumps don't load for some reason.
Can you try grabbing all following the instructions again.

Also upload your msinfo32.nfo file. To get this:

• Click on the Start
• Type msinfo32 into the Search programs and files box
• When it opens, go to File, Save
• Save as msinfo32.nfo and save in a place you will remember
• Let it finish the process of gathering and saving the system info
• Right click the .nfo file, click send to compressed (zipped) folder
• Upload the .zip file here.

It might be that the system is not capable of handling the memory intensive tasks

BTW, is it a desktop or a laptop?
Sounds like a laptop to me.

Is the system under its warranty?

Lett us know

You might want to lend some RAM from a friend or neighbor and see if it allows you to play the games.
BTW, Make a hard drive test from the hard drive manufacturers website

Run Disk Check for file system errors and bad sectors on it
→ Disk Check

Hard drive test both short and long with
→ SeaTools for Windows

You may also go through these
→ Hard Drive Diagnostic Procedure

2 GB is for basic tasks, you'd need more 2 GB for gaming.

How many sticks of ram do you have? From what I can find you have two slots for ram. Your specs indicate you can use up to 4 gig of ram. Two sticks of 2 gigs@ would help a lot for gaming if nothing is broke. If you can find the motherboard manual on line it would help you alot. This is not a gamer PC but more ram would help.
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HP Pavilion p6600 Desktop PC series - HP Pavilion p6640d Desktop PC Product Specifications - c02539290 - HP Business Support Center
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H IG41 uATX Mainboard Specs