BSODs randomly after installing Windows on new SSD

[Boozad]

Right, first off I'm noticing plenty of these:

Event[8611]:
  Log Name: System
  Source: Microsoft-Windows-Kernel-Processor-Power
  Date: 2015-07-23T20:52:53.850
  Event ID: 26
  Task: N/A
  Level: Information
  Opcode: Info
  Keyword: N/A
  User: S-1-5-18
  User Name: NT AUTHORITY\SYSTEM
  Computer: Jake-PC
  Description: 
Processor 0 in group 0 exposes the following:
3 idle state(s)
12 performance state(s)
[COLOR=red][B]8 throttle state(s)[/B][/COLOR]

Could you monitor your CPU temperatures please.

Also I'm still thinking along the line of there being a problem with your SSD, so going back to te original post and GokAy's suggesetion it may be worth switching to AHCI may be the way forward, the fact that the system still isn't writing crash dumps is strange.

 

[cantona7]

Do you mean change it back from AHCI to IDE?

I changed to AHCI mode as GokAy suggested, and after this the system changed from doing random BSODs as per the screenshots I posted a while back, to just completely switching off at random. So maybe it's better to switch back to IDE in the hope that BSODs start reoccurring, and that switching the dump settings from Kernel dump to mini dump as you recommended earlier will mean that dumps start being recorded?