This is bizarre.
Last night I decided to try and turn the Mac on and it worked!
And low and behold it is still working exactly 24 hours later! Today I did contact another Mac store who advised it could be a motherboard or power supply problem. I was planning to take in tomorrow but I am going to give it another day or so.
If it holds up I think it is software related and the only software I have installed in recent weeks, and now thinking back to the last time the problem happened before, was the installation and usage of Eye TV!
Could it really be that simple?
We will see.