BSOD - Right after start up... Works when it wants to!!

My laptop has given me problems as of late. I am experiencing random BSOD's after start up... I say random only b/c the laptop will work fine for a day or two and then go right back to BSOD problems. I have tried a system restore it works on safe mode & networking... currently its working on windows normal start up and so I wanted to take the time out and try to cure this problem before it begins to act up again. Please help, Thanx in advance Kaaz.

I am working on that now & I will return with the results. Thank you koolkat77... One question how do I post the results? Do I run another SF_Diagnostic_Tool or do I just let you know if the BSOD occurs again... Either way thanx for your support I really do appreciate you taking the time to help me find a solution to this problem. Thank you.

OhMyGoodness!
It took me like forever to kind of complete every thing on that list...
So here's the UPDATE.

McAfee Removal Tool - McAfee Uninstaller - COMPLETED SUCCESSFULLY

Microsoft Security Essentials - Full Scan COMPLETED SUCCESSFULLY KIND OF
-malware found and was prompted to download & run Windows Defender Offline
-Ran Windows Defender Offline from USB before start up. Full Scan completed no virus found. Re-started my computer & MSE found the same virus again & prompted WDO. Re-started computer ran WDO again same result... did this about 3x's then moved on to the next step.

Malwarebytes - COMPLETED SUCCESSFULLY
-found same virus as MSE TrojanDOS/Alureon.A rootkit:Alureon->Mbr::Alureon
-Quarantined/Removed

Good and Free system security combination - 90% Completed
-I found View device webpage but once there I didn't see anything for firewall/configure to select standard apply & exit, so that part wasn't done.
-added the WOT add-on - COMPLETED
-SuperAntiSpyware - COMPLETED

Startup Programs - Change - COMPLETED

SFC /SCANNOW Command - System File Checker - COMPLETED
-Windows Resource Protection did not find any intergrity violations.

Disk Check - COMPLETED

*now by this time i only experienced a BSOD once and this was in the beginning of this process and i haven't experienced it since & my computer was restarted at least 10x's already.
**I was also prompted to install a window update but Error(s)found: Code FFFFFFFE & I am unable to install this update.
***MSE & Malwarebytes still see the virus
****I ran another Dump File and attached it here along with the Malwarebytes report. Please see attachments.

I ran the rootkit utility & it successfully "cured" my problem.

When I tried to run the ESET Scan a msg came up stating "Can not get update. Is proxy configured?"

BUT

I was able to get my windows update install that i wasn't able to get before. So for the most part I have to say that my BSOD problem is solved and thank you so much again and again and again Thank you. Problem Solved!!