BSOD at random times daily, error 0x00000124

Here is what I have so far. I've been trying to figure this out as I go, so I'm not sure what information I provide is/isn't important. SF Diagnostic to follow.

BSOD happens anywhere from start up to after hours of intensive use, although it happens more frequently as use intensifies.

I have checked all drivers, detached all nonessential hardware, replaced avast antivirus with Microsoft security essentials, moved/reseated memory, and installed custom CPU fan, all to no avail.

When I check the error in Windbg with !errrec, the details always come up that there is a cache [read/write] error in bank 7, regardless of the processor core or process name. I suspect the processor may be faulty, but I want to make sure before I send it back to Intel. Running their processor diagnostic tool results in either a pass or a crash, but the system crashes so frequently I can't be certain the test has anything to do with it.

Code:

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Use !analyze -v to get detailed debugging information.

BugCheck 124, {0, fffffa8009b0e028, fe200000, 21136}

Probably caused by : GenuineIntel

Followup: MachineOwner
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Does the IPDT Full Functional test pass? Try an alternate CPU test:
CPU - Stress Test Using IntelBurnTest

If it passes, check your RAM:
RAM - Test with Memtest86+

You MUST run a minimum of 8 passes with MemTest86+

See if the system stays stable...if not, upload the new dmp file

It may be worth checking that no connections are shorting against the case.