BSOD randomly on the computer.

Here is the information:
Problem Event Name: BlueScreen
OS Version: 6.1.7601.2.1.0.768.3
Locale ID: 1033
Additional information about the problem:
BCCode: a
BCP1: 00000000000000DC
BCP2: 0000000000000002
BCP3: 0000000000000001
BCP4: FFFFF80002D05405
OS Version: 6_1_7601
Service Pack: 1_0
Product: 768_1
Files that help describe the problem:
C:\Windows\Minidump\120212-151289-01.dmp
C:\Users\Zane.User-PC\AppData\Local\Temp\WER-185812-0.sysdata.xml

I edited it, and I attached all of the dmp files. As you will see, the problems been going on for awhile. The last two or the most recent ones though.

Hello zaneo777.

Something is blocking the network, but from the data you have provided it is difficult to decide anything precisely.

Scan the system for possible virus infection.

• Anti-rootkit utility TDSSKiller
• Windows Defender Offline

upload your MSINFO32.nfo file.

1. Click on the start button
2. Type "msinfo32" (without quotes) in the search bar of the start menu, click the resulting link. It will open the System Information window.
3. File>Save. In the "File Name" filed, put "MSINFO32" (without Quote), give the save location to desktop, and click the "save" button.
4. Give the time for processing, it will save a .nfo file on your desktop.
5. Zip it, and upload it following the instruction.

And, next time, post it following the Blue Screen of Death (BSOD) Posting Instructions.

In almost all the dumps, there are some evidences of malware.

Scan the system for possible virus infection.

• Anti-rootkit utility TDSSKiller
• Windows Defender Offline

I cannot say anything against Norton Internet Security with certainty here, but it is a suggestion, do it at least as a test. Uninstall Norton and all Symentec products using Norton Removal tool. Use Microsoft Security Essentials as your antivirus with windows inbuilt firewall, and free MBAM as the on demand scanner.
Download and install those, and then run full system scans with both of them, one by one.

Also, the network driver is kinda old here.

Code:

Name    [00000007] Realtek PCIe GBE Family Controller
Driver    c:\windows\system32\drivers\rt64win7.sys (7.46.610.2011, 526.60 KB (539,240 bytes), 6/10/2011 6:34 AM)

update the network driver.
First, download the network card driver from manufactuer's website, Realtek.
Then reinstall the driver:

1. Click the Start Button, type "devmgmt.msc" (without quotation marks) in the Start Menu Search box and press Enter.
2. Double click to expand "Network adaptors".
3. Right click your network card and click Uninstall.
4. Check "Delete driver software for this device" check box, click OK.
5. Restart the computer
6. If windows does not auto configure the appropriate drivers at startup, install the downloaded one manually.

Let us know the results.