Random BSODs - Help Required with dump Files

As I mentioned the new install probably would not work. Its hardware
Boot the computer tell me about the beeps.
One beep
one long one short
two short etc

If a new install did not work, its hardware. Lets start with step one. Do it slowly and carefully.
Be sure you are not over heating
Make sure that the PSU is sufficient
Memory is a big cause, be sure that it was done correctly

I cant help more than this, everything is in the link that I gave you.
I can answer questions.

STOP 0x0000007F: UNEXPECTED_KERNEL_MODE_TRAP

Usual causes: Memory corruption, Hardware (memory in particular), Installing a faulty or mismatched hardware (especially memory) or a failure after installing it, 3rd party firewall, Device drivers, SCSI/network/BIOS updates needed, Improperly seated cards, Incompatible storage devices, Overclocking, Virus scanner, Backup tool, Bad motherboard, Missing Service Pack

Code:

  Microsoft (R) Windows Debugger Version 6.11.0001.404 AMD64
Copyright (c) Microsoft Corporation. All rights reserved.

Loading Dump File [C:\Users\richc46\AppData\Local\Temp\Temp1_Minidump[1].zip\110510-31640-01.dmp]
Mini Kernel Dump File: Only registers and stack trace are available
Symbol search path is: SRV*c:\symbols*http://msdl.microsoft.com/download/symbols
Executable search path is: 
Windows 7 Kernel Version 7600 MP (2 procs) Free x86 compatible
Product: WinNt, suite: TerminalServer SingleUserTS Personal
Built by: 7600.16617.x86fre.win7_gdr.100618-1621
Machine Name:
Kernel base = 0x82c45000 PsLoadedModuleList = 0x82d84570
Debug session time: Fri Nov  5 11:40:27.328 2010 (GMT-4)
System Uptime: 0 days 5:05:13.500
Loading Kernel Symbols
...............................................................
................................................................
.....................
Loading User Symbols
Loading unloaded module list
..............
*******************************************************************************
*                                                                             *
*                        Bugcheck Analysis                                    *
*                                                                             *
*******************************************************************************
Use !analyze -v to get detailed debugging information.
BugCheck 7F, {d, 0, 0, 0}
Probably caused by : ntkrnlmp.exe ( nt!KiSystemFatalException+f )
Followup: MachineOwner
---------
0: kd> !analyze -v
*******************************************************************************
*                                                                             *
*                        Bugcheck Analysis                                    *
*                                                                             *
*******************************************************************************
UNEXPECTED_KERNEL_MODE_TRAP (7f)
This means a trap occurred in kernel mode, and it's a trap of a kind
that the kernel isn't allowed to have/catch (bound trap) or that
is always instant death (double fault).  The first number in the
bugcheck params is the number of the trap (8 = double fault, etc)
Consult an Intel x86 family manual to learn more about what these
traps are. Here is a *portion* of those codes:
If kv shows a taskGate
        use .tss on the part before the colon, then kv.
Else if kv shows a trapframe
        use .trap on that value
Else
        .trap on the appropriate frame will show where the trap was taken
        (on x86, this will be the ebp that goes with the procedure KiTrap)
Endif
kb will then show the corrected stack.
Arguments:
Arg1: 0000000d, EXCEPTION_GP_FAULT
Arg2: 00000000
Arg3: 00000000
Arg4: 00000000
Debugging Details:
------------------

BUGCHECK_STR:  0x7f_d
CUSTOMER_CRASH_COUNT:  1
DEFAULT_BUCKET_ID:  VISTA_DRIVER_FAULT
PROCESS_NAME:  System
CURRENT_IRQL:  1c
UNALIGNED_STACK_POINTER:  82d63acd
LAST_CONTROL_TRANSFER:  from 82c7467f to 82c7e2bb
STACK_TEXT:  
82d63ae5 82c7467f badb0d00 00000000 20ffffff nt!KiSystemFatalException+0xf
82d63b78 00000000 00002600 00000000 0011e200 nt!KeAccumulateTicks+0x3c5

You have given me two reports. The first was the old 124 with the same information.The second was BC 7F. I have given you the causes for 7F , above
Again, memory comes up. Bios, also, comes up. This is something that should be handled by a professional. A little mistake when working on the Bios can make your computer an expensive paper weight. Mother Board can also be a cause.

I want to help as much as I can, but that 124 is a pain. You know as much as I do on it now. The 124 is the important one as it keeps popping up. We can use the BC codes of 7F etc, to look for hardware that is mentioned.

You are correct both reports show a 124, hardware error. You were there, if you feel that the BSOD was caused by the test, then you found the answer. That stress test was mentioned in the Code 124 post that I gave you a the beginning of all this; so its results are considred accurate. If that was indeed the cause you may need a new CPU.