0x0000003b BSOD - I'm out of ideas!

Sorry for the slight delay, I've been preparing myself for a job application.

Am I correct when I say some storage devices are connected to Asmedia ports? If not I would be surprised to see some Asmedia drivers back in this IRP (I/O Request Packet, communication method to have contact with other drivers and the OS).

Code:

8: kd> !irp ffffc6802cb0c010 1
Irp is active with 8 stacks 9 is current (= 0xffffc6802cb0c320)
 No Mdl: No System Buffer: Thread ffffc68025df1040:  Irp is completed.  
Flags = 00000000
ThreadListEntry.Flink = ffffc6802cb0c030
ThreadListEntry.Blink = ffffc6802cb0c030
IoStatus.Status = c00000bb
IoStatus.Information = 00000000
RequestorMode = 00000000
Cancel = 00
CancelIrql = 0
ApcEnvironment = 00
UserIosb = 00000000
UserEvent = 00000000
Overlay.AsynchronousParameters.UserApcRoutine = 00000000
Overlay.AsynchronousParameters.UserApcContext = 00000000
Overlay.AllocationSize = 00000000 - 00000000
CancelRoutine = 00000000   
UserBuffer = 00000000
&Tail.Overlay.DeviceQueueEntry = ffffc6802cb0c088
Tail.Overlay.Thread = ffffc68025df1040
Tail.Overlay.AuxiliaryBuffer = 00000000
Tail.Overlay.ListEntry.Flink = 00000000
Tail.Overlay.ListEntry.Blink = 00000000
Tail.Overlay.CurrentStackLocation = ffffc6802cb0c320
Tail.Overlay.OriginalFileObject = 00000000
Tail.Apc = 00000000
Tail.CompletionKey = 00000000
     cmd  flg cl Device   File     Completion-Context
 [N/A(0), N/A(0)]
            0  2 00000000 00000000 00000000-00000000    

			Args: 00000000 00000000 00000000 ffffffffc00000bb
 [N/A(0), N/A(0)]
            0  0 00000000 00000000 00000000-00000000    

			Args: 00000000 00000000 00000000 00000000
 [N/A(0), N/A(0)]
            0  0 00000000 00000000 00000000-00000000    

			Args: 00000000 00000000 00000000 00000000
 [N/A(0), N/A(0)]
            0  0 00000000 00000000 00000000-00000000    

			Args: 00000000 00000000 00000000 00000000
 [N/A(0), N/A(0)]
            0 10 00000000 00000000 00000000-00000000    

			Args: 00000000 00000000 00000000 00000000
 [IRP_MJ_PNP(1b), IRP_MN_START_DEVICE(0)]
            0 12 ffffc6802ca02880 00000000 fffff803439cd010-ffffaf8c7d9c41f0    
	      *** WARNING: Unable to verify timestamp for asmtxhci.sys
*** ERROR: Module load completed but symbols could not be loaded for asmtxhci.sys
 \Driver\asmtxhci	nt!ViFilterGenericCompletionRoutine
			Args: 00000000 00000000 00000000 00000000
 [IRP_MJ_PNP(1b), IRP_MN_START_DEVICE(0)]
            0 10 ffffc6802cb00ae0 00000000 fffff803439cd010-ffffaf8c7d9c45c0    
	      *** WARNING: Unable to verify timestamp for asmthub3.sys
*** ERROR: Module load completed but symbols could not be loaded for asmthub3.sys
*** WARNING: Unable to verify timestamp for ctxusbm.sys
*** ERROR: Module load completed but symbols could not be loaded for ctxusbm.sys
 \Driver\asmthub3	nt!ViFilterGenericCompletionRoutine
			Args: 00000000 00000000 00000000 00000000
 [IRP_MJ_PNP(1b), IRP_MN_START_DEVICE(0)]
            0 10 ffffc6802cb049e0 00000000 fffff80343302060-ffffc6802cb88fc0    
	       \DRIVER\VERIFIER_FILTER	nt!PnpDeviceCompletionRoutine
			Args: 00000000 00000000 00000000 00000000

Irp Extension present at 0xffffc6802cb0c320:

I'll still await diagnosis of the last dumps I attached though, please guys. The reason for this is that even after uninstalling the software which seems problematic - the Driver Verifier BSOD is BEFORE entering Windows.

My understanding is that the PC should get as far as the shell i.e. desktop before that happens. Is that correct?

No, the boot process exists of various phases.
Driver verifier is loaded as soon as ntoskrnl is called by Winload which is called after the boot manager is finished. Ntoskrnl has 2 phases of initialization. The first phase loads all BSOD messages, initializes driver verifier, creates some processes and does a few other things. The second phase ensures driver verifier is working and initializes components like the system time and drivers. Then smss.exe loads autochkdsk, registry hives, some dll's and some executables. Then winlogon.exe registers the user and userinit.exe runs the final scripts for both the user and the machine.

The login screen is 1 of the last steps in the boot process whilst driver verifier and all the drivers are loaded long before that. This is the reason why some users cannot log back in when driver verifier is enabled, some boot drivers are causing trouble in those situations.

Undelete? Why/how are they deleted?

Unless there's some task configured with disk cleanup, no minidump gets deleted (exception with the minidump limit of 50).

To answer your question, it might be possible. Deleting a file only marks the file as 'deleted' so it can be overwritten (which is why deleting 10's of thousands of files goes incredibly fast), if you have a program like Recuva installed you can undo the deleting.

If you do not have such a program installed, every action involving writing to the disk must be done on a different partition than the Windows partition, e.g. downloading, unpacking a zip, installing, etc., if you don't install it on a different partition the dumps will very likely be overwritten with no chance of a proper recovery.

Also, don't follow the command posted in the thread you linked. It looks to be a command I used some time ago which has a small issue resulting in not all requested files being collected.

Files from C:\Windows\Minidump are the ones needed.