Windows 7: Apparently Random BSOD (BCCode:f4 BCP1: 0000000000000003)

No problem, when you have time.
Re-seat the hardware, this can and does solve problems like yours.
Search for videos on how to do this, there are many.
This laptop may be similar to yours: Dell Vostro 3555 laptop - memory and hard drive upgrade

The event logs:
The windows error log service went into "stopped" state, or "started" is routine and not important.

This is either the Intel driver or (usually) a bad hard drive.

Same as above, but also may be HDD connector (re-seating might help) or bad motherboard.

Happens when you laptop crashes, not important.

Hard drive error.



This happens sometimes, check that MSE is up to date.
Can also be caused by HDD error.

Standard info, not important.

This is from a BSoD, can be used if the crashes aren't being reported, not important in your case.

Are there any System Event Logs from the last week?
Or does it end there?

Hi Dave76. Thanks again for the reply. I will tell you that after downgrading the Intel RST driver, the system has been running for a whole day now, zipping huge files, scanning for security threats, playing streaming audio, running a virtual machine, web browsers, etc., all at the same time. Looks promising.
Now, regarding the errors, the ones I sent you were the last ones on the file. As you can see, there are more than 8000 events logged in that file. I’m attaching here now the first events on the file. If you need me to get you more from the beginning or end of the file, please let me know:

Event[470]: (there are 5 other events just like this at the beginning)
Log Name: System
Source: Service Control Manager
Date: 2012-11-14T12:30:07.289
Event ID: 7000
Task: N/A
Level: Error
Opcode: N/A
Keyword: Classic
User: N/A
User Name: N/A
Computer: PCAC
Description:
The TDKLIB service couldn't start because of the following error:
The system can't find the specified file.

Event[584]: (more than 120 events like this)
Log Name: System
Source: Disk
Date: 2012-11-14T12:35:24.523
Event ID: 51
Task: N/A
Level: Warning
Opcode: N/A
Keyword: Classic
User: N/A
User Name: N/A
Computer: PCAC
Description:
Error detected on device \Device\Harddisk2\DR2 during a pagination operation.

Event[731]: (7 events like this)
Log Name: System
Source: Disk
Date: 2012-11-14T13:00:31.189
Event ID: 11
Task: N/A
Level: Error
Opcode: N/A
Keyword: Classic
User: N/A
User Name: N/A
Computer: PCAC
Description:
The driver detected a driver error on \Device\Harddisk1\DR3.

Event[1630]:
Log Name: System
Source: Microsoft-Windows-Kernel-Power
Date: 2012-11-14T15:59:56.002
Event ID: 41
Task: N/A
Level: Critical
Opcode: Information
Keyword: N/A
User: S-1-5-18
User Name: NT AUTHORITY\SYSTEM
Computer: PCAC
Description:
The system was restarted without a clean shutdown first. This error can be generated because the system stopped responding, it freezed or the power supply was suddently interrupted.

Event[1661]:
Log Name: System
Source: Microsoft-Windows-WER-SystemErrorReporting
Date: 2012-11-14T16:00:12.000
Event ID: 1005
Task: N/A
Level: Error
Opcode: N/A
Keyword: Classic
User: N/A
User Name: N/A
Computer: PCAC
Description:
Can't create a mini dump file from the whole dump file.

Event[1662]:
Log Name: System
Source: Microsoft-Windows-WER-SystemErrorReporting
Date: 2012-11-14T16:00:12.000
Event ID: 1001
Task: N/A
Level: Error
Opcode: N/A
Keyword: Classic
User: N/A
User Name: N/A
Computer: PCAC
Description:
The system was restarted after an error check. The performed error check was: 0x000000f4 (0x0000000000000003, 0xfffffa8008806b30, 0xfffffa8008806e10, 0xfffff80002bdadb0). A dump file was saved in: C:\Windows\MEMORY.DMP. Report ID: .

Event[1713]:
Log Name: System
Source: Service Control Manager
Date: 2012-11-14T16:03:00.738
Event ID: 7001
Task: N/A
Level: Error
Opcode: N/A
Keyword: Classic
User: N/A
User Name: N/A
Computer: PCAC
Description:
The DHCP client service depends on the Ancillary Function Driver for Winsock service, which couldn't start because of the following error:
One of the devices connected to the system isn't working.

Event[1714]:
Log Name: System
Source: Service Control Manager
Date: 2012-11-14T16:03:00.738
Event ID: 7001
Task: N/A
Level: Error
Opcode: N/A
Keyword: Classic
User: N/A
User Name: N/A
Computer: PCAC
Description:
The DNS client service depends on the inherited TDI NETIO controller support service, which couldn't start because of the following error:
One of the devices connected to the system isn't working.

Intel driver or bad HDD, that many error messages indicates a serious problem, hopefully they have stopped.
When you have a driver or bad HDD it can corrupt OS system files and cause all kinds of issues, including the OS can't recognize the HDD.

Check the Event log settings.
If you still aren't getting any new messages then you can 'Clear Log' as mentioned below.
To check the System Event Log settings.
1. Start Event Viewer.
2. In the console tree, expand Windows Logs and select System.
3. On the Action menu, click Properties.
4. In the General Tab, ensure 'Enable logging' is checked.
Maximum log size should be 20480
Under 'When maximum event log size is reached': select 'Overwrite events as needed (oldest events first)'
Click OK.

If you are still not getting new System Event Logs, you can 'Clear Log' on the same page.

You can post a few new ones, if you get any.
No need for any more older ones.

Hi Dave76. No new logs, and the system has been running for close to 36 hours now, without hiccups. Hopefully your suggestion to downgrade the driver has solved it for good.

I'll keep you posted if any additional errors occur, in which case I'll also proceed to the re-seating of the RAM, HDD and DVD. If after the weekend everything seems normal, I'll mark it as solved.

Thanks!

That's very good news.

Let us know how it's running after the weekend.

Hi Dave76. It seems that the driver was the problem. I'll let it work for a couple more of days and then close it if everything keeps working correctly. Thank you so much for all the help to you and all that contributed!!!

Great news, glad to hear it.

Let us know how it's doing, in a couple days.

Once again, thanks everybody, and specially Dave76. The laptop has been good so far, so I'll mark it as solved!

Glad to hear it.

You're welcome.
Unusual for Intel, but their RST driver above 11.2.0.1006 has been having stability issues, some systems can run 11.6.0.1030 but, not all.