OS Crash when rendering project

Question

When I am rendering a project the OS crashes.  It's not a blue screen.  It actually just disappears.  Then entire machine just shuts off.
The event viewer shows Event ID 41 (see event information below).  This is event it s new to the log.
Repro Steps:
- Copy any MTS file from my camera to the desktop (Canon VIXIA HF R21)
- add it to the timeline
- Render the file (render to youtube or locally as an avi)
- The render never completes.  It crashes.  The machine just turns off.  (I was trying to use PRE to create a DV-AVI to edit)
- It seems to fail at a specific step in the process.  Just not sure there is a log someplace for the render.
Additional info.
If I play any MTS file in the time line it flows nicely for about 20-30 seconds.  then the video gets jumpy.
I understand the minimum system requiremetns for HD editing is 4GB Ram.  I see that I have 2GB.
Question?
Is this a problem that I could fix by throwing money at? (obviously that answer is usually yes, but I mean simply adding memory)  I would hate to buy an additional 2-4 GB's of RAM only to find out that was not the problem.
It really feels like a step in the process is writing outside a buffer.  The OS just shuts down at that point.  It's not a reboot.  It just shuts off.  I have to manually restart the machine.
System Info
Hard Drive
WD6400AAKS SATA 3 Gb/s,  7200rpm, 16 MB Cache, 640 GB
System Information
Time of this report: 4/7/2011, 20:12:00
Machine name: IDK
Operating System: Windows 7 Home Premium 64-bit (6.1, Build 7601) Service Pack 1 (7601.win7sp1_rtm.101119-1850) (fully patched via Windows Update)
Language: English (Regional Setting: English)
System Manufacturer: HP-Pavilion
System Model: AW011AV-ABA p6250t
BIOS: BIOS Date: 05/06/09 11:31:10 Ver: 5.39
Processor: Intel(R) Core(TM)2 Quad CPU    Q8300  @ 2.50GHz (4 CPUs), ~2.5GHz
Available OS Memory: 2048MB RAM
Page File: 1413MB used, 2680MB available
Windows Dir: C:\Windows
DirectX Version: DirectX 11
DX Setup Parameters: Not found
User DPI Setting: Using System DPI
System DPI Setting: 96 DPI (100 percent)
DWM DPI Scaling: Disabled
DxDiag Version: 6.01.7601.17514 64bit Unicode
Display Devices
Card name: ATI Radeon HD 4300/4500 Series      
Manufacturer: ATI Technologies Inc.
Chip type: ATI display adapter (0x954F)
DAC type: Internal DAC(400MHz)
Device Key: Enum\PCI\VEN_1002&DEV_954F&SUBSYS_16131462&REV_00
Display Memory: 1274 MB
Dedicated Memory: 506 MB
Shared Memory: 767 MB
Current Mode: 1920 x 1080 (32 bit) (60Hz)
Monitor Name: HP 2159 Series Wide LCD Monitor
Monitor Model: HP 2159
Monitor Id: HWP282B
Native Mode: 1920 x 1080(p) (60.000Hz)
Output Type: DVI
Driver Name: aticfx64.dll,aticfx64.dll,aticfx32,aticfx32,atiumd64.dll,atidxx64.dll,atiumdag,atidxx32,a tiumdva,atiumd6a.cap,atitmm64.dll
Driver File Version: 8.17.0010.1070 (English)
Driver Version: 8.831.2.0
DDI Version: 10.1
Driver Model: WDDM 1.1
Driver Attributes: Final Retail
Driver Date/Size: 3/8/2011 21:55:52, 795136 bytes
Event Info
System
Provider
[ Name]
Microsoft-Windows-Kernel-Power
[ Guid]
{331C3B3A-2005-44C2-AC5E-77220C37D6B4}
EventID
41
Version
2
Level
1
Task
63
Opcode
0
Keywords
0x8000000000000002
John ...

Answer 1

I find that Merlot makes all my video look better. 
I went to Fry's and picked up a $19 heatsink.  It has the machine up and running.  The kids are "Happily" doing their homework again.
I'm now looking for a new machine for editing.  I'll read through some of the posts and see where I'll end up.  Looks like an i9 9xx proc with 6-8 GB of RAM. and two HDD's (OS and Data).  An industrial HVAC system to keep the entire thing cool.
GPU?  I'm sure it's important, I'd try to leverage that processor if I could.  But, PRE doesn't appear to have any settings, but I'm probably just missing something.
I'll dig around those articles and try to pull someting together.
John ....