Multiple BSOD, F4 and 7A, Computer will not produce a Minidump

I have already updated the OCZ firmware (helpfully suggested above) and have now updated the JMB36X Controller as well. I'm going to try running the programs that have crashed most often but as an initial test I ran a chkdsk on C:\ (which it refused to do previously) and it worked, report below in case it's relevant (I think it's all clear).

Log Name: Application
Source: Microsoft-Windows-Wininit
Date: 04/08/2013 15:34:57
Event ID: 1001
Task Category: None
Level: Information
Keywords: Classic
User: N/A
Computer: Mark-PC
Description:


Checking file system on C:
The type of the file system is NTFS.

A disk check has been scheduled.
Windows will now check the disk.

CHKDSK is verifying files (stage 1 of 5)...
195072 file records processed.

File verification completed.
613 large file records processed.

0 bad file records processed.

0 EA records processed.

54 reparse records processed.

CHKDSK is verifying indexes (stage 2 of 5)...
246762 index entries processed.

Index verification completed.
0 unindexed files scanned.

0 unindexed files recovered.

CHKDSK is verifying security descriptors (stage 3 of 5)...
195072 file SDs/SIDs processed.

Cleaning up 1062 unused index entries from index $SII of file 0x9.
Cleaning up 1062 unused index entries from index $SDH of file 0x9.
Cleaning up 1062 unused security descriptors.
Security descriptor verification completed.
25846 data files processed.

CHKDSK is verifying Usn Journal...
35045048 USN bytes processed.

Usn Journal verification completed.
CHKDSK is verifying file data (stage 4 of 5)...
195056 files processed.

File data verification completed.
CHKDSK is verifying free space (stage 5 of 5)...
12471449 free clusters processed.

Free space verification is complete.
CHKDSK discovered free space marked as allocated in the
master file table (MFT) bitmap.
CHKDSK discovered free space marked as allocated in the volume bitmap.
Windows has made corrections to the file system.

117218303 KB total disk space.
66958784 KB in 122141 files.
73260 KB in 25847 indexes.
0 KB in bad sectors.
300459 KB in use by the system.
65536 KB occupied by the log file.
49885800 KB available on disk.

4096 bytes in each allocation unit.
29304575 total allocation units on disk.
12471450 allocation units available on disk.

Internal Info:
00 fa 02 00 20 42 02 00 e0 1e 04 00 00 00 00 00 .... B..........
b7 01 00 00 36 00 00 00 00 00 00 00 00 00 00 00 ....6...........
00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 ................

Windows has finished checking your disk.
Please wait while your computer restarts.

Event Xml:
<Event xmlns="http://schemas.microsoft.com/win/2004/08/events/event">
<System>
<Provider Name="Microsoft-Windows-Wininit" Guid="{206f6dea-d3c5-4d10-bc72-989f03c8b84b}" EventSourceName="Wininit" />
<EventID Qualifiers="16384">1001</EventID>
<Version>0</Version>
<Level>4</Level>
<Task>0</Task>
<Opcode>0</Opcode>
<Keywords>0x80000000000000</Keywords>
<TimeCreated SystemTime="2013-08-04T14:34:57.000000000Z" />
<EventRecordID>32845</EventRecordID>
<Correlation />
<Execution ProcessID="0" ThreadID="0" />
<Channel>Application</Channel>
<Computer>Mark-PC</Computer>
<Security />
</System>
<EventData>
<Data>

Checking file system on C:
The type of the file system is NTFS.

A disk check has been scheduled.
Windows will now check the disk.

CHKDSK is verifying files (stage 1 of 5)...
195072 file records processed.

File verification completed.
613 large file records processed.

0 bad file records processed.

0 EA records processed.

54 reparse records processed.

CHKDSK is verifying indexes (stage 2 of 5)...
246762 index entries processed.

Index verification completed.
0 unindexed files scanned.

0 unindexed files recovered.

CHKDSK is verifying security descriptors (stage 3 of 5)...
195072 file SDs/SIDs processed.

Cleaning up 1062 unused index entries from index $SII of file 0x9.
Cleaning up 1062 unused index entries from index $SDH of file 0x9.
Cleaning up 1062 unused security descriptors.
Security descriptor verification completed.
25846 data files processed.

CHKDSK is verifying Usn Journal...
35045048 USN bytes processed.

Usn Journal verification completed.
CHKDSK is verifying file data (stage 4 of 5)...
195056 files processed.

File data verification completed.
CHKDSK is verifying free space (stage 5 of 5)...
12471449 free clusters processed.

Free space verification is complete.
CHKDSK discovered free space marked as allocated in the
master file table (MFT) bitmap.
CHKDSK discovered free space marked as allocated in the volume bitmap.
Windows has made corrections to the file system.

117218303 KB total disk space.
66958784 KB in 122141 files.
73260 KB in 25847 indexes.
0 KB in bad sectors.
300459 KB in use by the system.
65536 KB occupied by the log file.
49885800 KB available on disk.

4096 bytes in each allocation unit.
29304575 total allocation units on disk.
12471450 allocation units available on disk.

Internal Info:
00 fa 02 00 20 42 02 00 e0 1e 04 00 00 00 00 00 .... B..........
b7 01 00 00 36 00 00 00 00 00 00 00 00 00 00 00 ....6...........
00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 ................

Windows has finished checking your disk.
Please wait while your computer restarts.
</Data>
</EventData>
</Event>

Not yet had a BSOD but the system has frozen completely (and irrevocably) twice now and Java has frozen once but not taken the system with it.

The first freeze was while running Minecraft, javaw.exe stopped responding, however unlike the previous crashes I've had since this problem started Ctrl+Alt+Del still worked. It's entirely possible the crash was the result of a modified minecraft client, though it was perfectly stable before.

The next two crashes (the second of which I was attempting to induce) were while using Google Drive's spreadsheet program. After leaving it running for a while the system locked up, mouse and keyboard were unresponsive. State remained for over an hour before I turned the machine off and on.

My Java version is up to date.

My computer has not crashed in two days. The issue with Google Drive still persists but it doesn't appear to be something anyone here can offer help with and since I don't actually need Drive, I was just helping a friend re-design his spreadsheet, I think it would be appropriate to offer my thanks to everyone who has helped and to declare this thread solved.