Finally got through to HP Tech Support (for some reason my phone and my other-half's phone just kept ending the call when I attempted to call, even though we had sufficient credit, was able to finally get it working by using Skype as Skype allows 1-800 numbers for free even when using Skype from the UK).
In case it helps anyone else out there I was told:
That the fact that I recently updated my BIOS would help with overheating problems. That any overheating problems I have been experiencing could not be due to (for example) the motherboard or the graphics card, etc. That it may be wise to have my heat sink and fan replaced.
Mainly: I should (no surprises there) have my hard drive replaced ($155 - $200) .
For anyone living in the USA total costs (hard drive, heat sink, and fan) would be from $200 to $300 (labor and shipment costs included).