New HP laptop restarting "randomly".

Question

HP G62-455DX, Windows 7 Home Premium 64-bit.
After installing Window's Update's, but before the driver and HP Support Assistant update's, it began randomly
 restarting without showing any message, etc. Screen suddenly goes black and then a second later startup screen come's up.
I did the "out-of-box" restore, and then redid all the Update's...............still freaking happening.
Ran "Malicious Software Removal Tool", "Windows Defender", and "Trend Micro Titanium" on full scan's with all option's set
 to make it take longer and longer. Did memory and HDD check in BIOS, too, and ran "sfc /scannow" to attempt to fix error's in system
 file's. Nothing find's anything, or say's anything.
Can't find the error log, yet, but I imagine if I step back and look at it, it's going to look like someone using sign language for "#1".
This was not cheap, and there's no chance I can afford another. I have Accidental Protection on it, if that help's (it better, for it's price).
It's been less than 15 day's, and I am considering returning it and going to another company, both other than HP and BestBuy.
I know it's likely not all your company's fault, but I'm not going to blame anyone without blaming everyone. Even thinking about my
64 bit Ubuntu Linux install! Looking real pretty, now, compared to the amount of stress this has already caused.
Sorry for my attitude, I'm just really on edge over this. I've never bought a new computer, and  this is exactly what I was expecting.
 Feel free to talk nerdy, but keep it low to mid-level, I'm a geek, but not a Geeksquad geek.

Answer 1

Just finally found it with MS's W7 Help, here's the basis of 11 critical error's since the 16th:
=========== General ==========
The system has rebooted without cleanly shutting down first. This error could be caused if the
 system stopped responding, crashed, or lost power unexpectedly.
Log Name: System
Source: Kernel-Power   Logged: 2/18/2011 1:24:46 AM
Event ID: 41    Task Category: (63)
Level: Critical                   Keywords: (2)
User: SYSTEM                Computer: Tom
OpCode: Info
=========== Details ===========
- 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 
  - TimeCreated 
   [ SystemTime]  2011-02-18T07:24:46.125216900Z 
   EventRecordID 8040 
   Correlation 
  - Execution 
   [ ProcessID]  4 
   [ ThreadID]  8 
   Channel System 
   Computer Tom 
  - Security 
   [ UserID]  S-1-5-18 
- EventData 
  BugcheckCode 0 
  BugcheckParameter1 0x0 
  BugcheckParameter2 0x0 
  BugcheckParameter3 0x0 
  BugcheckParameter4 0x0 
  SleepInProgress false 
  PowerButtonTimestamp 0
========= END =========
So, maybe it's a faulty battery, or some..thing to do with it? IDK anymore, my brain is dead.